'132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:48:40 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:48:20 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasd + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors/timing (if any): Timing: real 0m0.011s user 0m0.006s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:47:18 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasd + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors/timing (if any): Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:47:00 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasd + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors (if any): Timing: real 0m0.011s user 0m0.008s sys 0m0.003s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:54 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd fsadlkfg sin(I)/0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors (if any): *** unknown function or error in formal parameters: *** ...sd=sdasadfasdfsadlkfgsin(I)/0 ^---- Timing: real 0m0.011s user 0m0.008s sys 0m0.004s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:38 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd fsadlkfg sin(I)/0 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? ? Goodbye! Errors (if any):...Done. *** unknown function or error in formal parameters: *** ...sd=sdasadfasdfsadlkfgsin(I)/0 ^---- Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:28 2005 Input: 2+2/(a slkdj fz z) + asd= sdasa dfasd fsadlkfg Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = ((sdasadfasdfsadlkfg + 2)*aslkdjfzz + 2)/aslkdjfzz ? Goodbye! Errors (if any):...Done. Timing: real 0m0.017s user 0m0.007s sys 0m0.004s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:46:14 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any):...Done. Timing: real 0m0.012s user 0m0.010s sys 0m0.001s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:45:57 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:...Done. Timing: real 0m0.013s user 0m0.006s sys 0m0.004s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:44:04 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.014s user 0m0.007s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:43:37 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.004s sys 0m0.007s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:43:21 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.005s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:40:31 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:40:06 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 256000000, primelimit = 500000 ? %1 = 4 ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.011s user 0m0.006s sys 0m0.005s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:39:39 2005 Input: 2+2 Output: Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 1: gp-2.2.11: command not found Timing: real 0m0.002s user 0m0.000s sys 0m0.001s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:39:02 2005 Input: 2+2 Output: GP/PARI CALCULATOR Version 2.2.11 (development CHANGES-1.1327) amd64 running linux (x86-64/GMP-4.1.4 kernel) 64-bit version compiled: Sep 29 2005, gcc-4.0.2 20050821 (prerelease) (Debian 4.0.1-6) (readline v5.0 enabled, extended help not available) Copyright (C) 2000-2005 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. parisize = 1024000000, primelimit = 500000 %1 = 4 Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.012s user 0m0.005s sys 0m0.006s '132.239' ************** PARI ***************** Host 132.239.145.210 (132.239.145.210) Time: Fri Sep 30 19:36:56 2005 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.008s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 15:22:02 2004 Input: 2 Output: 2  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 18:49:14 2004 Input: 2+21 Output: 23  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:27:42 2004 Input: prime(41561) Output: 500257  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:27:50 2004 Input: prime(42) Output: 181  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:32 2004 Input: prime(41561) Output: 500257  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:38 2004 Input: 18*19 Output: 342  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:41 2004 Input: 18*19 Output: 342  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:28:48 2004 Input: 2+6 Output: 8  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Tue Sep 7 20:29:33 2004 Input: 2+3 Output: 5  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Tue Sep 7 20:43:31 2004 Input: isprime(1907) Output: 1  Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Tue Sep 7 21:00:32 2004 Input: factorint(1907^64+1) Output: Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 1: 3602 Killed /usr/bin/gp-2.1 -q Timing: real 0m21.006s user 0m20.995s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:05:22 2004 Input: print(2+2) Output: 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:06:36 2004 Input: print(2+2) Output: 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:06:44 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:09:24 2004 Input: factor(9458094850943) Output: An error occured in the PARI system call. ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:09:33 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:02 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:03 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:08 2004 Input: factor(9458094850943) Output: An error occured in the PARI system call. ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:10:12 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:11 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:15 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:23 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:29 2004 Input: factor(9458094850943) Output:  [2549 1] [3710511907 1]   Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:34 2004 Input: factor(12) Output:  [2 2] [3 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:40 2004 Input: print("'hello'") Output: 'hello'  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.001s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:49 2004 Input: print("'hello'"); factor(098093860943) Output: 'hello'  [13 2] [580437047 1]   Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:12:54 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:14:54 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:15:12 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:15:13 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:15:25 2004 Input: print("'hello'"); 2+2 Output: 'hello' 4  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:16:15 2004 Input: print("'[;35m]'") Output: '[;35m]'  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 21:16:21 2004 Input: print("'[0;35m]'") Output: ']'  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:07:01 2004 Input: sum(j=1,10000,isprime(j)) Output: 1229  Errors (if any) and Timing Info: Timing: real 0m0.047s user 0m0.044s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:07:25 2004 Input: sum(j=1,10000,isprime(3*j+1)) Output: 1610  Errors (if any) and Timing Info: Timing: real 0m0.062s user 0m0.057s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:07:49 2004 Input: sum(j=1,15000,isprime(3*j+1)) Output: 2325  Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.086s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:08:07 2004 Input: sum(j=1,15000,isprime(3*j+2)) Output: 2348  Errors (if any) and Timing Info: Timing: real 0m0.090s user 0m0.086s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:08:49 2004 Input: sum(j=1,20000,isprime(3*j+1)) Output: 3014  Errors (if any) and Timing Info: Timing: real 0m0.117s user 0m0.111s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:09:01 2004 Input: sum(j=1,20000,isprime(3*j+2)) Output: 3041  Errors (if any) and Timing Info: Timing: real 0m0.117s user 0m0.112s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:09:35 2004 Input: sum(j=1,25000,isprime(3*j+2)) Output: 3710  Errors (if any) and Timing Info: Timing: real 0m0.145s user 0m0.140s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:09:43 2004 Input: sum(j=1,25000,isprime(3*j+1)) Output: 3681  Errors (if any) and Timing Info: Timing: real 0m0.144s user 0m0.139s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:10:16 2004 Input: sum(j=1,30000,isprime(3*j+1)) Output: 4339  Errors (if any) and Timing Info: Timing: real 0m0.172s user 0m0.168s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:10:25 2004 Input: sum(j=1,30000,isprime(3*j+2)) Output: 4373  Errors (if any) and Timing Info: Timing: real 0m0.173s user 0m0.171s sys 0m0.001s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:11:04 2004 Input: sum(j=1,100,isprime(3*j+2)) Output: 32  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:11:09 2004 Input: sum(j=1,100,isprime(3*j+1)) Output: 28  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:08 2004 Input: 2+2 Output: Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:18 2004 Input: 2+2 Output: 1 1  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:36 2004 Input: 2+2 Output: START STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:14:56 2004 Input: 9205809545 Output: START STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:15:17 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:17:28 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:04 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:05 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:06 2004 Input: 9205809545 Output: START 9205809545 STOP  Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:18:46 2004 Input: 9205809545 Output: GP/PARI CALCULATOR Version 2.2.7 (alpha) x86_64 running linux (portable C kernel) 64-bit version compiled: Sep 3 2004, gcc-3.3.4 (Debian 1:3.3.4-9) (readline not compiled in, extended help available) Copyright (C) 2003 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. realprecision = 38 significant digits seriesprecision = 16 significant terms format = g0.38 parisize = 8000000, primelimit = 500000 START %1 = 9205809545 STOP Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.009s user 0m0.002s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:08 2004 Input: 9205809545 Output: ** WARNING: Computation used more memory than allowed. ** ### Usage: /usr/bin/gp [options] [GP files] Options are: [-f] Faststart: do not read .gprc [-q] Quiet mode: do not print banner and history numbers [-p primelimit] Precalculate primes up to the limit [-s stacksize] Start with the PARI stack of given size (in bytes) [--emacs] Run as if in Emacs shell [--help] Print this message [--test] Test mode. No history, wrap long lines (bench only) [--texmacs] Run as if using TeXmacs frontend [--version] Output version info and exit [--version-short] Output version number and exit Errors (if any) and Timing Info: Timing: real 0m0.004s user 0m0.002s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:19 2004 Input: 9205809545 Output: ? START 9205809545 ? STOP ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:36 2004 Input: 9205809545 Output: ? 9205809545 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:19:44 2004 Input: factor(9468946849) Output: ? [101 1] [93751949 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:20:21 2004 Input: factor(9468946849) Output: GP/PARI CALCULATOR Version 2.2.7 (alpha) x86_64 running linux (portable C kernel) 64-bit version compiled: Sep 3 2004, gcc-3.3.4 (Debian 1:3.3.4-9) (readline not compiled in, extended help available) Copyright (C) 2003 The PARI Group PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER. Type ? for help, \q to quit. Type ?12 for how to get moral (and possibly technical) support. realprecision = 38 significant digits seriesprecision = 16 significant terms format = g0.38 parisize = 8000000, primelimit = 500000 ? %1 = [101 1] [93751949 1] ? Goodbye! Errors (if any) and Timing Info:Reading GPRC: /etc/gprc ...Done. Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 65.96.167.57 (65.96.167.57) Time: Tue Sep 7 22:20:41 2004 Input: factor(9468946849) Output: ? [101 1] [93751949 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:22:19 2004 Input: 1.0/(23*29) Output: ? 0.0014992503748125937031484257871064467766 ? Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:40:08 2004 Input: isprime(43) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:41:47 2004 Input: isprime(1807) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:42:09 2004 Input: factor(1807) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:43:55 2004 Input: factor(326443) Output: ? [13 1] [25111 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:44:01 2004 Input: factor(3263443) Output: ? [3263443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:45:38 2004 Input: factor(2*3*7*43*13*139*3263443+1) Output: ? [547 1] [607 1] [1033 1] [31051 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:46:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:46:29 2004 Input: factor(2*3*7*43*13*139+1) Output: ? [3263443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:46:57 2004 Input: factor(2*3*7*43*13*139*3263443+1) Output: ? [547 1] [607 1] [1033 1] [31051 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:47:21 2004 Input: factor(2*3*7*43*13*139*3263443*547+1) Output: ? [31 1] [1201073 1] [156461741 1] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:47:39 2004 Input: factor(2*3*7*43*13*139*3263443*547*31+1) Output: ? [11 1] [1791173 1] [9165807481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:47:46 2004 Input: factor(2*3*7*43*13*139*3263443*547*31*11+1) Output: ? [1986523172862990763 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:48:22 2004 Input: factor(2*3*7*43*13*139*3263443*547*31*11*1986523172862990763+1) Output: ? [3946274316321643878601150356160331407 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:49:40 2004 Input: factor(2*3*7*43*13*139*3263443*547*31*11*1986523172862990763*3946274316321643878601150356160331407+1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 4242 Killed /usr/bin/gp -q --emacs Timing: real 0m21.015s user 0m20.957s sys 0m0.044s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:50:32 2004 Input: factor(2+1) Output: ? [3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:50:51 2004 Input: factor(2*3+1) Output: ? [7 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:01 2004 Input: factor(2*3*7+1) Output: ? [43 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:11 2004 Input: factor(2*3*7*43+1) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:27 2004 Input: factor(2*3*7*43*13+1) Output: ? [53 1] [443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:51:49 2004 Input: factor(2*3*7*43+1) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:00 2004 Input: factor(2*3*7*43*13+1) Output: ? [53 1] [443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:11 2004 Input: factor(2*3*7*43*13*53+1) Output: ? [5 1] [248867 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:22 2004 Input: factor(2*3*7*43*13*53*5+1) Output: ? [6221671 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:52:40 2004 Input: factor(2*3*7*43*13*53*5*6221671+1) Output: ? [38709183810571 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:06 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571+1) Output: ? [139 1] [25621 1] [420743244646304724409 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:20 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139+1) Output: ? [2801 1] [2897 1] [489241 1] [119812279 1] [437881957 1] ? Errors (if any) and Timing Info: Timing: real 0m0.035s user 0m0.026s sys 0m0.009s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:34 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801+1) Output: ? [11 1] [1009 1] [241139351 1] [217973650939627698919 1] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.028s sys 0m0.011s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:53:58 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11+1) Output: ? [17 1] [1949 1] [193681376161759185018665262907 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:10 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17+1) Output: ? [5471 1] [19940260577270817092450816057441 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:22 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17*5471+1) Output: ? [52662739 1] [11333415626130617914714237072849 1] ? Errors (if any) and Timing Info: Timing: real 0m0.024s user 0m0.020s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:36 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11*17+1) Output: ? [5471 1] [19940260577270817092450816057441 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:42 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801*11+1) Output: ? [17 1] [1949 1] [193681376161759185018665262907 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:47 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139*2801+1) Output: ? [11 1] [1009 1] [241139351 1] [217973650939627698919 1] ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.028s sys 0m0.013s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:54:53 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571*139+1) Output: ? [2801 1] [2897 1] [489241 1] [119812279 1] [437881957 1] ? Errors (if any) and Timing Info: Timing: real 0m0.036s user 0m0.030s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:07 2004 Input: factor(2*3*7*43*13*53*5*6221671*38709183810571+1) Output: ? [139 1] [25621 1] [420743244646304724409 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:19 2004 Input: factor(2*3*7*43*13*53*5*6221671+1) Output: ? [38709183810571 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:33 2004 Input: factor(2*3*7*43*13*53*5+1) Output: ? [6221671 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:38 2004 Input: factor(2*3*7*43*13*53+1) Output: ? [5 1] [248867 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:43 2004 Input: factor(2*3*7*43*13+1) Output: ? [53 1] [443 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:50 2004 Input: factor(2*3*7*43+1) Output: ? [13 1] [139 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 22:55:55 2004 Input: factor(2*3*7+1) Output: ? [43 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:12:25 2004 Input: 1.0/(3*7) Output: ? 0.047619047619047619047619047619047619048 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:12:38 2004 Input: 1.0/(13*7) Output: ? 0.010989010989010989010989010989010989011 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:12:48 2004 Input: 1.0/(19*17) Output: ? 0.0030959752321981424148606811145510835913 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:13:01 2004 Input: 1.0/19*17 Output: ? 0.89473684210526315789473684210526315789 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:13:57 2004 Input: 1.0/(19*17) Output: ? 0.0030959752321981424148606811145510835913 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:14:25 2004 Input: 1.0/(3*11) Output: ? 0.030303030303030303030303030303030303030 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:14:37 2004 Input: 1.0/(3*13) Output: ? 0.025641025641025641025641025641025641026 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:14:59 2004 Input: 1.0/(3*17) Output: ? 0.019607843137254901960784313725490196078 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:15:33 2004 Input: 1.0/(3*19) Output: ? 0.017543859649122807017543859649122807017 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:16:00 2004 Input: 1.0/(3*23) Output: ? 0.014492753623188405797101449275362318841 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Tue Sep 7 23:16:44 2004 Input: 1.0/(3*29) Output: ? 0.011494252873563218390804597701149425287 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:12:56 2004 Input: factor(x^8192+x^4096+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.267s user 0m0.165s sys 0m0.013s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:13:38 2004 Input: factor(x^1024+x^512+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.133s user 0m0.122s sys 0m0.010s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:13:51 2004 Input: factor(x^64+x^32+1) Output: ? [x^2 - x + 1 1] [x^2 + x + 1 1] [x^4 - x^2 + 1 1] [x^8 - x^4 + 1 1] [x^16 - x^8 + 1 1] [x^32 - x^16 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.014s user 0m0.008s sys 0m0.008s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:16:22 2004 Input: factor(x^64+1) Output: ? [x^64 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.013s sys 0m0.003s ************** PARI ***************** Host 80.170.145.228 (80.170.145.228) Time: Wed Sep 8 11:40:18 2004 Input: ?ellj Output: ? ellj(x): elliptic j invariant of x. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 80.170.145.228 (80.170.145.228) Time: Wed Sep 8 11:40:32 2004 Input: ??ellj Output: ? ellj(x):  elliptic j-invariant. x must be a complex number with positive imaginary part, or convertible into a power series or a p-adic number with positive valuation.  The library syntax is jell(x,prec).  ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.022s sys 0m0.011s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 11:45:23 2004 Input: factorint(1907^2+1907+1) Output: ? [13 1] [19 1] [14731 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:00:46 2004 Input: factorint(1907^2-1907+1) Output: ? [3 1] [7 1] [73 1] [2371 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:01:52 2004 Input: factorint(1907^4-1907^2+1) Output: ? [313 1] [42253074481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:02:23 2004 Input: isprime(42253074481); factorint(1907^4-1907^2+1) Output: ? ? [313 1] [42253074481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:02:32 2004 Input: isprime(42253074481); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:03:21 2004 Input: factorint(1907^4-1907^2+1) Output: ? [313 1] [42253074481 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:03:31 2004 Input: factorint(1907^8-1907^4+1) Output: ? [1153 1] [58834969 1] [2578343098231993 1] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.017s sys 0m0.007s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:04:40 2004 Input: factorint(1907^16-1907^8+1) Output: ? [30011460673 1] [2824227165916129 1] [360931120130402792118884353 1] ? Errors (if any) and Timing Info: Timing: real 0m1.064s user 0m1.044s sys 0m0.021s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:06:46 2004 Input: factorint(1907^16-1907^8+1) Output: ? [30011460673 1] [2824227165916129 1] [360931120130402792118884353 1] ? Errors (if any) and Timing Info: Timing: real 0m1.064s user 0m1.044s sys 0m0.020s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:07:43 2004 Input: factorint(1907^32-1907^16+1) Output: ? [5886721 1] [52584193 1] [1672632769 1] [2723997117982753 1] [663569271483415189828884374287238562011527002801300848278885776481 1] ? Errors (if any) and Timing Info: Timing: real 0m9.437s user 0m9.411s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Wed Sep 8 12:12:34 2004 Input: factorint(1907^64-1907^32+1) Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 8778 Killed /usr/bin/gp -q --emacs Timing: real 0m21.041s user 0m20.995s sys 0m0.005s ************** PARI ***************** Host 128.250.6.243 (128.250.6.243) Time: Wed Sep 8 12:42:44 2004 Input: ?tate Output: ? ? Errors (if any) and Timing Info: *** tate: unknown identifier. Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 24.125.49.176 (24.125.49.176) Time: Wed Sep 8 12:50:34 2004 Input: % MathType!MTEF!2!1!+- % faaafaart1ev1aaat0uyJj1BTfMBaerbuLwBLnharmWu51MyVXgaru % WqVvNCPvMCaebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hh % bbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0- % yq-He9q8qqQ8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaa % eaaakeaadaWcaaqaaiaaikdacaaIWaaabaGaaGymaiaac6cacaaIXa % aaaiabgUcaRmaalaaabaGaaGOmaiaaikdaaeaacaGGOaGaaGymaiaa % c6cacaaIXaGaaiykamaaCaaaleqabaGaaGOmaaaaaaGccqGHRaWkda % WcaaqaaiaaikdacaaI0aaabaGaaiikaiaaigdacaGGUaGaaGymaiaa % cMcadaahaaWcbeqaaiaaiodaaaaaaOGaey4kaSYaaSaaaeaacaaIYa % GaaGOnaaqaaiaacIcacaaIXaGaaiOlaiaaigdacaGGPaWaaWbaaSqa % beaacaaI0aaaaaaakiabgUcaRmaalaaabaGaaGOmaiaaiIdaaeaaca % GGOaGaaGymaiaac6cacaaIXaGaaiykamaaCaaaleqabaGaaGynaaaa % aaGccqGH9aqpaaa!4CF1! [ frac{{20}}{{1.1}} + frac{{22}}{{(1.1)^2 }} + frac{{24}}{{(1.1)^3 }} + frac{{26}}{{(1.1)^4 }} + frac{{28}}{{(1.1)^5 }} = ] Output: WARNING: PARI command contains unsafe command '%', so it will not be executed. ************** PARI ***************** Host 128.227.95.245 (128.227.95.245) Time: Wed Sep 8 13:03:35 2004 Input: 2^445 Output: ? 90854840536950861318665475986000566794205170085914757535186274897579911014174740415773881339220445695095315200783272241691825203576832 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 128.227.95.245 (128.227.95.245) Time: Wed Sep 8 13:03:39 2004 Input: 2^4454564 Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.010s user 0m0.003s sys 0m0.008s ************** PARI ***************** Host 194.42.0.254 (194.42.0.254) Time: Wed Sep 8 15:33:48 2004 Input: SetVerbose("Code",true); print("gf2 n151 QR"); print(MinimumDistance(QRCode(GF(2),151))); Output: ? ? gf2 n151 QR ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SetVerbose("Code",tr ^-------------------- *** unknown function or error in formal parameters: print(MinimumDistance( *** QRCode(GF(2),151))); ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 140.247.241.194 (140.247.241.194) Time: Wed Sep 8 17:11:49 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 140.247.241.194 (140.247.241.194) Time: Wed Sep 8 17:39:30 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:54:43 2004 Input: (1.0)/(3*29) Output: ? 0.011494252873563218390804597701149425287 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:01 2004 Input: (1.0)/(3*31) Output: ? 0.010752688172043010752688172043010752688 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:28 2004 Input: (1.0)/(3*37) Output: ? 0.0090090090090090090090090090090090090090 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:37 2004 Input: (1.0)/(3*41) Output: ? 0.0081300813008130081300813008130081300813 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:55:50 2004 Input: (1.0)/(3*43) Output: ? 0.0077519379844961240310077519379844961240 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:56:58 2004 Input: (1.0)/(3*7) Output: ? 0.047619047619047619047619047619047619048 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:57:18 2004 Input: (1.0)/(11*7) Output: ? 0.012987012987012987012987012987012987013 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:57:37 2004 Input: (1.0)/(13*7) Output: ? 0.010989010989010989010989010989010989011 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:57:52 2004 Input: (1.0)/(17*7) Output: ? 0.0084033613445378151260504201680672268907 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:58:12 2004 Input: (1.0)/(19*7) Output: ? 0.0075187969924812030075187969924812030075 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:58:33 2004 Input: (1.0)/(23*7) Output: ? 0.0062111801242236024844720496894409937888 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:58:52 2004 Input: (1.0)/(29*7) Output: ? 0.0049261083743842364532019704433497536946 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:59:12 2004 Input: (1.0)/(31*7) Output: ? 0.0046082949308755760368663594470046082949 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 21:59:59 2004 Input: (1.0)/(37*7) Output: ? 0.0038610038610038610038610038610038610038 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:00:19 2004 Input: (1.0)/(41*7) Output: ? 0.0034843205574912891986062717770034843205 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:01:05 2004 Input: (1.0)/(43*7) Output: ? 0.0033222591362126245847176079734219269103 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:23 2004 Input: (1.0)/(43*17) Output: ? 0.0013679890560875512995896032831737346101 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:32 2004 Input: (1.0)/(43*71) Output: ? 0.00032754667540124467736652472977399279397 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:40 2004 Input: (1.0)/(43*19) Output: ? 0.0012239902080783353733170134638922888617 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.174.253 (137.99.174.253) Time: Wed Sep 8 22:05:49 2004 Input: (1.0)/(43*83) Output: ? 0.00028019052956010086859064163631269263099 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:19:37 2004 Input: gp Output: ? gp ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:21:44 2004 Input: M-x gpman Output: ? M - xgpman ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:27:13 2004 Input: prime(1) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:27:23 2004 Input: prime(2) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:27:32 2004 Input: prime(367) Output: ? 2477 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:28:00 2004 Input: prime(9876425) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:28:09 2004 Input: prime(987642) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:28:14 2004 Input: prime(987) Output: ? 7793 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:44:12 2004 Input: prime(987) Output: ? 7793 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:45:18 2004 Input: listcreate(15) listput(l,x,{15}) Output: ? List([]) ? ? Errors (if any) and Timing Info: *** unexpected character: listput(l,x,{15}) ^------ Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:45:27 2004 Input: listcreate(15) Output: ? List([]) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.171.95 (137.99.171.95) Time: Thu Sep 9 00:45:48 2004 Input: listcreate(15,9) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: listcreate(15,9) ^--- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:14:29 2004 Input: x^2360+1 Output: ? x^2360 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.074s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:14:38 2004 Input: factor(x^2360+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m1.055s user 0m0.960s sys 0m0.014s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:15:07 2004 Input: factor(x^590+1) Output: ? [x^2 + 1 1] [x^8 - x^6 + x^4 - x^2 + 1 1] [x^116 - x^114 + x^112 - x^110 + x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90 + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1 1] [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.794s user 0m0.783s sys 0m0.010s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:15:42 2004 Input: factor(x^295-1) Output: ? [x - 1 1] [x^4 + x^3 + x^2 + x + 1 1] [x^58 + x^57 + x^56 + x^55 + x^54 + x^53 + x^52 + x^51 + x^50 + x^49 + x^48 + x^47 + x^46 + x^45 + x^44 + x^43 + x^42 + x^41 + x^40 + x^39 + x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1 1] [x^232 - x^231 + x^227 - x^226 + x^222 - x^221 + x^217 - x^216 + x^212 - x^211 + x^207 - x^206 + x^202 - x^201 + x^197 - x^196 + x^192 - x^191 + x^187 - x^186 + x^182 - x^181 + x^177 - x^176 + x^173 - x^171 + x^168 - x^166 + x^163 - x^161 + x^158 - x^156 + x^153 - x^151 + x^148 - x^146 + x^143 - x^141 + x^138 - x^136 + x^133 - x^131 + x^128 - x^126 + x^123 - x^121 + x^118 - x^116 + x^114 - x^111 + x^109 - x^106 + x^104 - x^101 + x^99 - x^96 + x^94 - x^91 + x^89 - x^86 + x^84 - x^81 + x^79 - x^76 + x^74 - x^71 + x^69 - x^66 + x^64 - x^61 + x^59 - x^56 + x^55 - x^51 + x^50 - x^46 + x^45 - x^41 + x^40 - x^36 + x^35 - x^31 + x^30 - x^26 + x^25 - x^21 + x^20 - x^16 + x^15 - x^11 + x^10 - x^6 + x^5 - x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.274s user 0m0.264s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:27:22 2004 Input: factor(x^295+1) Output: ? [x + 1 1] [x^4 - x^3 + x^2 - x + 1 1] [x^58 - x^57 + x^56 - x^55 + x^54 - x^53 + x^52 - x^51 + x^50 - x^49 + x^48 - x^47 + x^46 - x^45 + x^44 - x^43 + x^42 - x^41 + x^40 - x^39 + x^38 - x^37 + x^36 - x^35 + x^34 - x^33 + x^32 - x^31 + x^30 - x^29 + x^28 - x^27 + x^26 - x^25 + x^24 - x^23 + x^22 - x^21 + x^20 - x^19 + x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 1] [x^232 + x^231 - x^227 - x^226 + x^222 + x^221 - x^217 - x^216 + x^212 + x^211 - x^207 - x^206 + x^202 + x^201 - x^197 - x^196 + x^192 + x^191 - x^187 - x^186 + x^182 + x^181 - x^177 - x^176 - x^173 + x^171 + x^168 - x^166 - x^163 + x^161 + x^158 - x^156 - x^153 + x^151 + x^148 - x^146 - x^143 + x^141 + x^138 - x^136 - x^133 + x^131 + x^128 - x^126 - x^123 + x^121 + x^118 - x^116 + x^114 + x^111 - x^109 - x^106 + x^104 + x^101 - x^99 - x^96 + x^94 + x^91 - x^89 - x^86 + x^84 + x^81 - x^79 - x^76 + x^74 + x^71 - x^69 - x^66 + x^64 + x^61 - x^59 - x^56 - x^55 + x^51 + x^50 - x^46 - x^45 + x^41 + x^40 - x^36 - x^35 + x^31 + x^30 - x^26 - x^25 + x^21 + x^20 - x^16 - x^15 + x^11 + x^10 - x^6 - x^5 + x + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.276s user 0m0.271s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 21:31:43 2004 Input: factorint(2232) Output: ? [2 3] [3 2] [31 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:31:45 2004 Input: (2231^59+1)/2232 Output: ? 163222661996330643021625900568133161837019233177601029720608640382119886410226092659450274961762280231835890055195857302400497410073832844638125717198765425036184230570146534199935658385314011571 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:34:26 2004 Input: isprime(20862329904766606481) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.009s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:34:39 2004 Input: isprime(158491610535765167876531) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Thu Sep 9 22:34:48 2004 Input: factorint(158491610535765167876531) Output: ? [57993871231 1] [2732902756301 1] ? Errors (if any) and Timing Info: Timing: real 0m0.037s user 0m0.018s sys 0m0.008s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:48:40 2004 Input: factor(x^590+1) Output: ? [x^2 + 1 1] [x^8 - x^6 + x^4 - x^2 + 1 1] [x^116 - x^114 + x^112 - x^110 + x^108 - x^106 + x^104 - x^102 + x^100 - x^98 + x^96 - x^94 + x^92 - x^90 + x^88 - x^86 + x^84 - x^82 + x^80 - x^78 + x^76 - x^74 + x^72 - x^70 + x^68 - x^66 + x^64 - x^62 + x^60 - x^58 + x^56 - x^54 + x^52 - x^50 + x^48 - x^46 + x^44 - x^42 + x^40 - x^38 + x^36 - x^34 + x^32 - x^30 + x^28 - x^26 + x^24 - x^22 + x^20 - x^18 + x^16 - x^14 + x^12 - x^10 + x^8 - x^6 + x^4 - x^2 + 1 1] [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.797s user 0m0.783s sys 0m0.016s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:53:40 2004 Input: factor((x^590+1)/(x^118+1)) Output: ? [x^8 - x^6 + x^4 - x^2 + 1 1] [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.657s user 0m0.648s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:54:50 2004 Input: factor(((x^590+1)*(x^2+1))/((x^118+1)*(x^10+1))) Output: ? [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.612s user 0m0.589s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 01:54:50 2004 Input: factor(((x^590+1)*(x^2+1))/((x^118+1)*(x^10+1))) Output: ? [x^464 + x^462 - x^454 - x^452 + x^444 + x^442 - x^434 - x^432 + x^424 + x^422 - x^414 - x^412 + x^404 + x^402 - x^394 - x^392 + x^384 + x^382 - x^374 - x^372 + x^364 + x^362 - x^354 - x^352 - x^346 + x^342 + x^336 - x^332 - x^326 + x^322 + x^316 - x^312 - x^306 + x^302 + x^296 - x^292 - x^286 + x^282 + x^276 - x^272 - x^266 + x^262 + x^256 - x^252 - x^246 + x^242 + x^236 - x^232 + x^228 + x^222 - x^218 - x^212 + x^208 + x^202 - x^198 - x^192 + x^188 + x^182 - x^178 - x^172 + x^168 + x^162 - x^158 - x^152 + x^148 + x^142 - x^138 - x^132 + x^128 + x^122 - x^118 - x^112 - x^110 + x^102 + x^100 - x^92 - x^90 + x^82 + x^80 - x^72 - x^70 + x^62 + x^60 - x^52 - x^50 + x^42 + x^40 - x^32 - x^30 + x^22 + x^20 - x^12 - x^10 + x^2 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.624s user 0m0.597s sys 0m0.010s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 02:07:30 2004 Input: (2231^590 + 1)*(2231^2 + 1)/((2231^118 + 1)*(2231^10 + 1)*1181*3541*794141) Output: ? 152239467487306026593551353106829467321781361064829543830227647403047242045700775476673654553868753880021057508691908000001391740442071688072434466375575485748317837485753412695904810308200594164860524353679491978402955893758988326558400376157170485876867086105812404700757868823510542752837826226111932399000172536861868978875095313074133573615526034977583290589516289267877248468764977622081393447191188331545128337997802868037204077477512825055415549948918088502025077849384166521229640479883402200098172568576327910839357127568019000412137771318377222332410557757022848604473806772575524626925232148671746603706899893433135031992515275229190171162920832157912487117182699946163659004703867744216467220315870672997512174923491664667307890509643481028129804066262238762617889866259995244445902889703365494945721247513028529261415341437924553183315606124604295262128990123637457508180599811046819758004378824542372053968483778108436617221910350620966331498151814912017861990287224325900793917807841988453035169500888178253287329499464150264836917836310283169284633792900629258484597242732991958836509460835876934624219815867976941997653420777217097385231715179326142666940272996800443770161204333271514334607377973713613556745295869467680546669147460151139063751078960945320677683451830373692686729529077085369663160067442936905894492384549891677692463979055159211220064873311427866537300959780092417153560566777594023221512396026971679430277151074559627218712102892045975723723775784123781157741049081221968422852845557960852136850695490901 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 02:09:50 2004 Input: x^20+1 Output: ? x^20 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 02:10:14 2004 Input: factor(x^20+1) Output: ? [x^4 + 1 1] [x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s ************** PARI ***************** Host 129.199.2.17 (129.199.2.17) Time: Fri Sep 10 08:39:19 2004 Input: ellinit([1,1,1,1,1]) Output: ? [1, 1, 1, 1, 1, 5, 3, 5, 4, -47, -665, -316, 103823/316, [-1.0000000000000000000000000000000000000, -0.12500000000000000000000000000000000000 - 1.1110243021644486062614302094260909771*I, -0.12500000000000000000000000000000000000 + 1.1110243021644486062614302094260909771*I]~, 3.8328305468038347928735039871096291388, -1.9164152734019173964367519935548145694 + 1.3916292718175425841570799922317030886*I, -1.1955120413393023640413217701950360471 + 8.918031641082844838 E-39*I, 0.59775602066965118202066088509751802357 - 1.2537215372422377533513109583343891468*I, 5.3338791828486541826811913789892565008] ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:13:51 2004 Input: 2230*(2231^295-1)/((2231^59-1)*(2231^5-1))/(4721*19471*46039264566131) Output: ? 167940315153702432375800550695229369802403980212020936540259277386301886139899965850294715404772422200103359497599991953309634334858953018972021070772995260207885334729065209558128776159343815628721611750691433489559906717450468487233739869084476698195634119486497201899925079549881583325141977446684624550061229847855152734492297951120716209806767305572829258556811641599326480657213226998688494649694877519120183485969243561892592052074915016200409593875204158346787559570588377248309813739653262124718520478309678094281396072053429254461125028388709076700759699551662680271551958618121975135692205436155119491493065240782926014063234138310426062848381326663489783293969970306926492857860261635568109767043121582573607424358149713141362184621437161133061 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:14:09 2004 Input: 2230*(2231^295-1)/((2231^59-1)*(2231^5-1)*(4721*19471*46039264566131)) Output: ? 167940315153702432375800550695229369802403980212020936540259277386301886139899965850294715404772422200103359497599991953309634334858953018972021070772995260207885334729065209558128776159343815628721611750691433489559906717450468487233739869084476698195634119486497201899925079549881583325141977446684624550061229847855152734492297951120716209806767305572829258556811641599326480657213226998688494649694877519120183485969243561892592052074915016200409593875204158346787559570588377248309813739653262124718520478309678094281396072053429254461125028388709076700759699551662680271551958618121975135692205436155119491493065240782926014063234138310426062848381326663489783293969970306926492857860261635568109767043121582573607424358149713141362184621437161133061 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:18:40 2004 Input: factor(x^1180+1) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m0.967s user 0m0.958s sys 0m0.009s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:19:03 2004 Input: factor(x^4+1) Output: ? [x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:19:12 2004 Input: factor(x^20+1) Output: ? [x^4 + 1 1] [x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:36:30 2004 Input: factor(x^20+1) Output: ? [x^4 + 1 1] [x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:37:09 2004 Input: factor((x^236 + 1)/(x^4 + 1)) Output: ? [x^232 - x^228 + x^224 - x^220 + x^216 - x^212 + x^208 - x^204 + x^200 - x^196 + x^192 - x^188 + x^184 - x^180 + x^176 - x^172 + x^168 - x^164 + x^160 - x^156 + x^152 - x^148 + x^144 - x^140 + x^136 - x^132 + x^128 - x^124 + x^120 - x^116 + x^112 - x^108 + x^104 - x^100 + x^96 - x^92 + x^88 - x^84 + x^80 - x^76 + x^72 - x^68 + x^64 - x^60 + x^56 - x^52 + x^48 - x^44 + x^40 - x^36 + x^32 - x^28 + x^24 - x^20 + x^16 - x^12 + x^8 - x^4 + 1 1] ? Errors (if any) and Timing Info: Timing: real 0m0.136s user 0m0.132s sys 0m0.003s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 11:39:23 2004 Input: (2231^20+1)/(2*1153*10743331537*41*4890161) Output: ? 1878824047044678338579426144223282103202441641 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 12:07:03 2004 Input: (2231^472 + 1)/(2231^8 + 1)/(168977*33111732097*1047346707857) Output: ? 2992078726034666586133825914560578840832725607767432512727806091296194352812432948820950122145853537677146536089674328445387481433924707505110028919336070072681098595682038314384229819731756909916779655818428801034873891023857620017986040746628367888419227411882449110379063258827834365579702247126007087132865321061743713263186074942062859145316351896035257991751404963017344954273513364016272733762410030753503973839352851151365389468127929667585549632416913951528937480036163202936133494469100337615259279079785923554412883529366583611740473228592554724150961808212146209968715514284535368549959563557408087783119909185326751472413687608816658208855671874066816444126256958371451369914905874286202622279861722411797593566927423186439331899953310662921538563400159829873331290271597332229617243410194452582765111480043368685607017056538026409481910362302108082035625648328876610759104471816438432588144685735057942153072799148566464856331386321196172981062461122950774565987250645412431113621997382412520701724045149778242674991795027899200232624778429275564782087669637068205170091907826083830032463128986917474149964287738021024918104465618615092410571027799320899477528727371355921722362096710136184406894231636508536926157841359340885716225733554769373543154392472416849274814573059527989267328023060614038046394893237996942433961624251577438668584342858009303108104050914294345407458665820536131154871530318083222342255767156076096686319163194621591224011564330846501151952663238783365511995283251344928697520599625312491051764745034073279793/34679463603235908986129 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 12:08:11 2004 Input: (2231^2360 + 1)*(2231^8 + 1)/((2231^472 + 1)*(2231^40 + 1))/(33111732097*1047346707857) Output: ? 6534350810739941660477885247723695990155975625432947134500952799537260269232294238335828404157769790020633146704872673362520289815480674831035721022923679729211132381568833686610541422639460039284043499003516410502548881620114578474070459039094404975510573004150915154718575939386346806090876320654018600797133907663012135322536606615273291553411106817415340008392340646172657224255420589448366471979302643354784902187296508841135044214477571295507397028255474593596993300921498500126984761309864354118605741691780983814965451436605530019892984540966540280743485538556474934772583068298583356002861716033444201286039383093608501427940571081781364087831247445775398538484303355037506780906696148749700532351674454883819748703339905248308887330116793519841085516178986692481633064078999423054890013672240678974136960466330285563773784678413667657884262553313761105436562581374235265002362813533645741442621395574754264751022738388465437842898503168627996241189018140285138338923305429934295996316597844901382711475410781557860409717119332442668432565768246992511032669853839585440444346847155419836295875036797761196773857313527314413935268549472266739373498801664116442471269693659893446996429356851313702300446649885312347972772269593424641055838098466495969919490590414005181696674425163108862561958186678269541797784738132433346147958127240916368734489956487249773960178847449408768834375433737991106624634885057145144206661626319776850401661035402593220292891595523890728116678361115370291543668838167456726880161942870186526482160928301350945058519521777924861911253309901220911798924243678034072468446747336555151840252335207750687555721315792757742851870112351334256040614926215786273408661720675598187871943905687072524343539495475883866658102203102568645273610379340551984255150951943649839473826516237607552698438964222505652130081551715490224303502474618234611619566647957472707737515353651264184966632660955473833447794141797464011458110777081703414506791100250652756063931401175282170217909571333858386470520521764787695920858693270968084972487391845139251088349829799648827096937196170532105797465649672791044922204584521967081229641870533293650436708868126708797124707193592871934126250286010803832861908278032601693398577813701266557890222567967251942619661269107249559368161644847255727531934160320666574834831722085955216339995872175546681881663406039670619722084697047879391674642780208620167533084318267276750031609795820856151592514993119726050655815739817604474889565068159388602879529562876945635084915945759910302649205300606388695528487098380631446323877860728177316847167067832050965109497579166002695981037435243975525799650795964292777790972048912977411098366875326632516533164996422601697438886205751526869128971424331969243286950133046081047749046154140092249862911691493747108707650227794221178829891298434313516524998208821371720344678412045624992054908366425191977123232882381603821510559428000723362504504934541626881369333462903781104327155985292189976286687813827502826246199380250341776286418341180819125965266920006635264414014373046122570434141324867211929732173071149109412627120909801017608249434952907105988316382198392460152471697496062725376409560[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.015s sys 0m0.003s ************** PARI ***************** Host 67.169.20.252 (67.169.20.252) Time: Fri Sep 10 12:08:43 2004 Input: (2231^2360 + 1)*(2231^8 + 1)/((2231^472 + 1)*(2231^40 + 1)*33111732097*1047346707857) Output: ? 6534350810739941660477885247723695990155975625432947134500952799537260269232294238335828404157769790020633146704872673362520289815480674831035721022923679729211132381568833686610541422639460039284043499003516410502548881620114578474070459039094404975510573004150915154718575939386346806090876320654018600797133907663012135322536606615273291553411106817415340008392340646172657224255420589448366471979302643354784902187296508841135044214477571295507397028255474593596993300921498500126984761309864354118605741691780983814965451436605530019892984540966540280743485538556474934772583068298583356002861716033444201286039383093608501427940571081781364087831247445775398538484303355037506780906696148749700532351674454883819748703339905248308887330116793519841085516178986692481633064078999423054890013672240678974136960466330285563773784678413667657884262553313761105436562581374235265002362813533645741442621395574754264751022738388465437842898503168627996241189018140285138338923305429934295996316597844901382711475410781557860409717119332442668432565768246992511032669853839585440444346847155419836295875036797761196773857313527314413935268549472266739373498801664116442471269693659893446996429356851313702300446649885312347972772269593424641055838098466495969919490590414005181696674425163108862561958186678269541797784738132433346147958127240916368734489956487249773960178847449408768834375433737991106624634885057145144206661626319776850401661035402593220292891595523890728116678361115370291543668838167456726880161942870186526482160928301350945058519521777924861911253309901220911798924243678034072468446747336555151840252335207750687555721315792757742851870112351334256040614926215786273408661720675598187871943905687072524343539495475883866658102203102568645273610379340551984255150951943649839473826516237607552698438964222505652130081551715490224303502474618234611619566647957472707737515353651264184966632660955473833447794141797464011458110777081703414506791100250652756063931401175282170217909571333858386470520521764787695920858693270968084972487391845139251088349829799648827096937196170532105797465649672791044922204584521967081229641870533293650436708868126708797124707193592871934126250286010803832861908278032601693398577813701266557890222567967251942619661269107249559368161644847255727531934160320666574834831722085955216339995872175546681881663406039670619722084697047879391674642780208620167533084318267276750031609795820856151592514993119726050655815739817604474889565068159388602879529562876945635084915945759910302649205300606388695528487098380631446323877860728177316847167067832050965109497579166002695981037435243975525799650795964292777790972048912977411098366875326632516533164996422601697438886205751526869128971424331969243286950133046081047749046154140092249862911691493747108707650227794221178829891298434313516524998208821371720344678412045624992054908366425191977123232882381603821510559428000723362504504934541626881369333462903781104327155985292189976286687813827502826246199380250341776286418341180819125965266920006635264414014373046122570434141324867211929732173071149109412627120909801017608249434952907105988316382198392460152471697496062725376409560[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.014s sys 0m0.005s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Fri Sep 10 14:55:36 2004 Input: (2231^59-1)/(2230*709*259666907*3357332933*59353538419519*3171594949246999313) Output: ? 1404068190735005451359636488128071856652539859763273187307160085592018868940146247873543293002704545982762705521681970806906289969544542871853 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:23:38 2004 Input: 5.0^5 Output: ? 3125.0000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:24:06 2004 Input: (5.0^5)^5 Output: ? 298023223876953125.00000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:31:53 2004 Input: 53125.0^5 Output: ? 423150360584259033203125.00000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Fri Sep 10 15:35:08 2004 Input: 5^5 Output: ? 3125 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 140.247.245.210 (140.247.245.210) Time: Fri Sep 10 15:49:58 2004 Input: factor(409809845) Output: ? [5 1] [89 1] [920921 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 216.51.235.246 (216.51.235.246) Time: Sat Sep 11 01:37:02 2004 Input: x/3-3x/4=1/12 Output: ? 1/3*x - 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x/4=1/12. Timing: real 0m0.272s user 0m0.004s sys 0m0.011s ************** PARI ***************** Host 216.51.235.246 (216.51.235.246) Time: Sat Sep 11 01:37:03 2004 Input: x/3-3x/4=1/12 Output: ? 1/3*x - 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: x/4=1/12. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 68.163.241.150 (68.163.241.150) Time: Sun Sep 12 00:11:11 2004 Input: -0.02y + 0.12(6000-y)= 0.11y Output: ? -0.020000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: y+0.12(6000-y)=0.11y. Timing: real 0m0.016s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 68.163.241.150 (68.163.241.150) Time: Sun Sep 12 00:11:50 2004 Input: -0.02y+0.12(6000-y)=0.11y Output: ? -0.020000000000000000000000000000000000000 ? Errors (if any) and Timing Info: *** Warning: unused characters: y+0.12(6000-y)=0.11y. Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 63.241.65.90 (63.241.65.90) Time: Sun Sep 12 00:24:44 2004 Input: y=2*x+3 x Output: ? 2*x + 3 ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:41:33 2004 Input: e=ellinit([0,0,0,17,0]); print(e.j" "e.disc" "e.tors" "ellglobalred(e)); Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: print(e.j" "e.disc" "e.tors" "ellglobalred( ^-------------------- Timing: real 0m0.071s user 0m0.005s sys 0m0.007s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:41:53 2004 Input: e=ellinit([0,0,0,17,0]); print(e.j" "e.disc" "e.tors"); Output: ? ? ? Errors (if any) and Timing Info: *** expected character: '"' instead of: ...e.j" "e.disc" "e.tors"); ^ *** Warning: run-away string. Closing it. Timing: real 0m0.010s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:42:15 2004 Input: e=ellinit([0,0,0,17,0]); print(e.j" "e.disc" "e.tors); Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: print(e.j" "e.disc" "e.tors); ^------ Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:42:27 2004 Input: e=ellinit([0,0,0,17,0]); e.tors Output: ? ? ? Errors (if any) and Timing Info: *** unknown member function: e.tors ^---- Timing: real 0m0.010s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:42:43 2004 Input: e=ellinit([0,0,0,17,0]); elltors(e) Output: ? ? [2, [2], [[0, 0]]] ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:43:17 2004 Input: e=ellinit([0,0,0,17,0]); ellglobalred(e) Output: ? ? [18496, [1, 0, 0, 0], 2] ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:43:44 2004 Input: e=ellinit([0,0,0,17,0]); factor(ellglobalred(e)[1]) Output: ? ? [2 6] [17 2] ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 129.194.8.73 (129.194.8.73) Time: Sun Sep 12 05:44:47 2004 Input: e=ellinit([0,0,0,17,0]); elllseries(e,1) Output: ? ? 3.6523718207373173530224734019481378047 ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.095s user 0m0.090s sys 0m0.004s ************** PARI ***************** Host 80.104.0.185 (80.104.0.185) Time: Sun Sep 12 08:14:27 2004 Input: 123 Output: ? 123 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 80.104.0.185 (80.104.0.185) Time: Sun Sep 12 08:14:52 2004 Input: 123 Output: ? 123 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 35.9.26.234 (35.9.26.234) Time: Sun Sep 12 15:33:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.056s user 0m0.004s sys 0m0.009s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:08:11 2004 Input: 1.10^1/3 Output: ? 0.36666666666666666666666666666666666667 ? Errors (if any) and Timing Info: Timing: real 0m0.065s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:08:29 2004 Input: 1.10^(1/3) Output: ? 1.0322801154563671592135852250097016117 ? Errors (if any) and Timing Info: Timing: real 0m0.040s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:09:55 2004 Input: 1.10^(3) Output: ? 1.3310000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:10:50 2004 Input: 0.9^(3) Output: ? 0.72899999999999999999999999999999999999 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:12:12 2004 Input: 1-(0.9^(3)) Output: ? 0.27100000000000000000000000000000000001 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:15:53 2004 Input: (1-.271)^(1/3) Output: ? 0.90000000000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:30:01 2004 Input: (-.99^3)+3*(-.99) Output: ? -3.9402990000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:30:36 2004 Input: (--1.01^3)+3*(-1.01) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (--1.01^3)+3*(-1.01) ^------------------- Timing: real 0m0.019s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 16:30:43 2004 Input: (-1.01^3)+3*(-1.01) Output: ? -4.0603010000000000000000000000000000000 ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 17:38:55 2004 Input: .04/.2551 Output: ? 0.15680125441003528028224225793806350451 ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Sun Sep 12 18:04:07 2004 Input: .04/.2551 Output: ? 0.15680125441003528028224225793806350451 ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 24.185.209.9 (24.185.209.9) Time: Sun Sep 12 20:30:20 2004 Input: 3578! Output: ? 1568147836345296343478655129144157738870498552100811568167073349024510094437388767101964723816127436799607650129576815186229608117951009415448018446658496909148985526889467538595150875712554908186778536452963456074412430243271703699624545756485663063182991850154025327315159372377794486304427408694681303207914448740594666358311506058737180004692085244327282183594315845251808961019288849800895470367494882640199759568046896384034969267618235789741414417476798217595382228643594475577638009379197216861488894939895794062484198132052553545335771930652655407597984297962604717840693900784479377353819882351629557175568714402323518530809257516922391357296800337131865134835002030205442326200401237987719255946784099255361332571189389657865444700891011514839453034603031627252617215824038289313205976764560981633044470543564880629084889498201227694074057229172636850686181179491601426961976484595368332864896850181084262438985283980635477005179405212283510513842952920136820976666534030625699069362928099884296540925358039571496091497943753150990690102879317241973060028911257070195411992467838661630426110874168995817766161418934632890075720737109370172085760406254302856724945276518396734559101537837788578627657921314821006349279330090637868051887086156420269834855684851439286766760643461083014651115417659796952763106204434406570047122763416800898182946002214609517201002936826308801844900083771708164635526982789134188997904260382299913827716357546937234398282583837875978409346800605349417960400465045320094979984226929331661607021419305672456449107829974444880965145304849901674288555489468783471983301580587691766092911297105203236074261748598115198276778058062294062170208192747018139313410218395480265457198139426707056009366628814228983915798043581761983137188223032345256122289524596049946428020020814575251582344889415206829883124778107699675350756024182829759106100652153682753872734657703650780360599230592249969450133356179723819120583906026015395321921706074209058924233195537345596354261871685324559256840698298489806517053229407795857527655976431340377029221101953943440863600798985971313578961245601305443783098331493375774975358732001725450764767991232528833356075725836251406374010861275842274276727633894743690029420721775949760837999759310289964610967770507580226378060038902144520888337249179241621965530323377220936354785168332333258442563246192018562320811267234963253611684291927056137912874680132328866684363320804830280738369674867581646918215125950445523500979693303950547131013105398381750510259495595430369855519738957971022996197272721661725136984926957012403948604099575552020557496242197981100997935383658596290878251737376138107115415993330005748642288665213070506056430167239297139424738583042725983130969987264898503644455875938347806030375389318193101183097863852290155464934349090235599560381355927694899897333501408970705937430326837211837174628108167774055925857692895871030982575826489644128189083183152400674394245555444887061992322024430513433659512622029097847229647709596078207141904014649664931829899842639783006934443508170759096629606364202518880920275555073348394521969268480676153300402636104060334677530550660285161394798716009457462214517[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.198s user 0m0.030s sys 0m0.009s ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 13 00:57:50 2004 Input: 3490529510847650949147849619903898133417764638493387843990820577*32769132993266709549961999190834461413177642967992942539798288533 Output: ? 114381625757888867669235818371971231334378737347588181505441310531117958673000181729623470563958705058989075147599290026879543541 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 13 01:14:18 2004 Input: 3490529510847650949147849619903898133417764638493387843990820577**9007 mod (32769132993266709549961999190834461413177642967992942539798288533) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...7764638493387843990820577**9007mod(3276913299 ^-------------------- Timing: real 0m0.019s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 13 01:15:50 2004 Input: 3490529510847650949147849619903898133417764638493387843990820577*9007 mod (32769132993266709549961999190834461413177642967992942539798288533) Output: ? 31439199304204792098974681526474410487693806098909944310825320937039 ? Errors (if any) and Timing Info: *** Warning: unused characters: mod(32769132993266709549961999190834461413177642967992942539798288533). Timing: real 0m0.017s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 01:56:34 2004 Input: 2+2 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:06 2004 Input: prime(12345678) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:16 2004 Input: prime(1234568) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:26 2004 Input: prime(123458) Output: ? ? Errors (if any) and Timing Info: *** not enough precomputed primes Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:32 2004 Input: prime(23458) Output: ? 267667 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:38:47 2004 Input: prime(25) Output: ? 97 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:39:02 2004 Input: prime(5) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:39:09 2004 Input: primes(5) Output: ? [2, 3, 5, 7, 11] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 24.117.130.176 (24.117.130.176) Time: Mon Sep 13 03:39:22 2004 Input: primes(55) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.008s sys 0m0.001s ************** PARI ***************** Host 199.171.142.1 (199.171.142.1) Time: Mon Sep 13 10:52:26 2004 Input: factor(7751391910122739843887037070559590001412606) Output: ? [2 1] [11 1] [23269 1] [15141862388356611496151799840129845017 1] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 14:31:49 2004 Input: (2231^590 + 1)*(2231^2 + 1)/((2231^118 + 1)*(2231^10 + 1))/(1181*3541*794141) Output: ? 152239467487306026593551353106829467321781361064829543830227647403047242045700775476673654553868753880021057508691908000001391740442071688072434466375575485748317837485753412695904810308200594164860524353679491978402955893758988326558400376157170485876867086105812404700757868823510542752837826226111932399000172536861868978875095313074133573615526034977583290589516289267877248468764977622081393447191188331545128337997802868037204077477512825055415549948918088502025077849384166521229640479883402200098172568576327910839357127568019000412137771318377222332410557757022848604473806772575524626925232148671746603706899893433135031992515275229190171162920832157912487117182699946163659004703867744216467220315870672997512174923491664667307890509643481028129804066262238762617889866259995244445902889703365494945721247513028529261415341437924553183315606124604295262128990123637457508180599811046819758004378824542372053968483778108436617221910350620966331498151814912017861990287224325900793917807841988453035169500888178253287329499464150264836917836310283169284633792900629258484597242732991958836509460835876934624219815867976941997653420777217097385231715179326142666940272996800443770161204333271514334607377973713613556745295869467680546669147460151139063751078960945320677683451830373692686729529077085369663160067442936905894492384549891677692463979055159211220064873311427866537300959780092417153560566777594023221512396026971679430277151074559627218712102892045975723723775784123781157741049081221968422852845557960852136850695490901 ? Errors (if any) and Timing Info: Timing: real 0m0.028s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 14:51:10 2004 Input: (2231^2360 + 1)*(2231^8 + 1)/((2231^472 + 1)*(2231^40 + 1)) Output: ? 6534350810739941660477885247723695990155975625432947134500952799537260269232294238335828404157769790020633146704872673362520289815480674831035721022923679729211132381568833686610541422639460039284043499003516410502548881620114578474070459039094404975510573004150915154718575939386346806090876320654018600797133907663012135322536606615273291553411106817415340008392340646172657224255420589448366471979302643354784902187296508841135044214477571295507397028255474593596993300921498500126984761309864354118605741691780983814965451436605530019892984540966540280743485538556474934772583068298583356002861716033444201286039383093608501427940571081781364087831247445775398538484303355037506780906696148749700532351674454883819748703339905248308887330116793519841085516178986692481633064078999423054890013672240678974136960466330285563773784678413667657884262553313761105436562581374235265002362813533645741442621395574754264751022738388465437842898503168627996241189018140285138338923305429934295996316597844901382711475410781557860409717119332442668432565768246992511032669853839585440444346847155419836295875036797761196773857313527314413935268549472266739373498801664116442471269693659893446996429356851313702300446649885312347972772269593424641055838098466495969919490590414005181696674425163108862561958186678269541797784738132433346147958127240916368734489956487249773960178847449408768834375433737991106624634885057145144206661626319776850401661035402593220292891595523890728116678361115370291543668838167456726880161942870186526482160928301350945058519521777924861911253309901220911798924243678034072468446747336555151840252335207750687555721315792757742851870112351334256040614926215786273408661720675598187871943905687072524343539495475883866658102203102568645273610379340551984255150951943649839473826516237607552698438964222505652130081551715490224303502474618234611619566647957472707737515353651264184966632660955473833447794141797464011458110777081703414506791100250652756063931401175282170217909571333858386470520521764787695920858693270968084972487391845139251088349829799648827096937196170532105797465649672791044922204584521967081229641870533293650436708868126708797124707193592871934126250286010803832861908278032601693398577813701266557890222567967251942619661269107249559368161644847255727531934160320666574834831722085955216339995872175546681881663406039670619722084697047879391674642780208620167533084318267276750031609795820856151592514993119726050655815739817604474889565068159388602879529562876945635084915945759910302649205300606388695528487098380631446323877860728177316847167067832050965109497579166002695981037435243975525799650795964292777790972048912977411098366875326632516533164996422601697438886205751526869128971424331969243286950133046081047749046154140092249862911691493747108707650227794221178829891298434313516524998208821371720344678412045624992054908366425191977123232882381603821510559428000723362504504934541626881369333462903781104327155985292189976286687813827502826246199380250341776286418341180819125965266920006635264414014373046122570434141324867211929732173071149109412627120909801017608249434952907105988316382198392460152471697496062725376409560[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.012s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:51:25 2004 Input: (r1+b)*sin w3 = x2-x3+(r1+a)*(x1-x2+r1*sin w1)/(r1+a) Output: ? sinw1*r1^2 + (sinw1*b + (-x3 + x1))*r1 + (-x3 + x1)*b ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:51:48 2004 Input: (r1+b)*sin(w3) = x2-x3+(r1+a)*(x1-x2+r1*sin(w1))/(r1+a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:52:18 2004 Input: (r1+b)*sin(w3) = x2-x3+(r1+a)*(x1 - x2 + r1*sin(w1))/(r1+a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 14:52:33 2004 Input: (2231^1180 + 1)*(2231^4 + 1)/((2231^236 + 1)*(2231^20 + 1)*198241) Output: ? 1289459611275041988195210056585206806410614084401135640479222664045769803591479690589717250628933460238307683337743645320339109228658943102343982115804448039233769992702578660444097102749918320340496288615167272422272379035481129224408741120123060633692817472406046988439452102203287959094815737110537691461874612805826793594075312453312968242778332100458437125673193379975931037064432110582767389977175612492393277539339744992094632099663885400758083900295190968549713896692958238574068888519018229346775417031722016125463201059730056703802804593518003521063911362932655632842008839899080544855503991771638642004164198129115480948843643820523789774352780610631114486522017869777461789993174649739094191335437704484177831242563949137031177943172811683858038790678569607858584220926893871795219838949150359526494044964470909496367876787866746320183625778761692644288518243530397384396547182256665167216304974969831373883366950933890318902922727340003762162113057889466370396883353544593047853142065591064803810488301183812747116340049386741364251144723947724119744045366782599827038640833816813508545524699558279735717481168569356350676805263349555599713747952874214769431466210013977287072133383364932859198544023793310419123285068298336070004787238695911938909700570537098346340491665553063998784474454161236911031840755337060581977681559962122670603754590598825568152740584854970612183933837874292716173072442936834101358188825490484369762849853108302033020223818808366127539168245624264464650554132670608278496939617008439302281320194114542205403777512385100038930034556715403151466036429661746992286310824650498732301746810128719185087093394926835604196015481609742101938982272000709437795472290874168456500316722612336016886476849700907316525206912306597386194441886873751591175573840163309814383160746362518400215087927991511089076291223297660110284881250544994303953041087974253934597024738438478477055360710506018704493335097484819208348847552668908442669888461558339812986365601959317027821972696038310903998111633164357379655640624289630886984712380123230308926635948294510536082796236853126251730091089211452890931680803323760411906469252262765014919017599368945227117703011625303913839499607952380984480817987350416403596260580581048766268751267980180944101655545053910056681340620023358494552404889493936818897398638536529861238810491507564596427454099716918690555584398852276288317134008602972664360303771682100411165070906789601758922723215836150877013163996628861999711660397392091971276225766687797899017718051709732552633122078712780353937390733719786158223050833770894698981549222005547082262483271803898663216500668723882082424201229010112432910392928477008055582517060405503932038412451480399585926077262102319937797345470755500358109056901019453751194562475815349091214534321493144904989115254862258310372856766455307486129497558829470061525458150084364948511232833683350699737351774282400205295937445856524938565236610331007570210527187394906814667251416126174766596677311815215382560438544236362437425990226574062165431012050930752880377419881319502057443979190101560674711643681 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:52:33 2004 Input: (r1 + b) * sin(w3) = x2 - x3 + (r1 + a) * (x1 - x2 + r1*sin(w1))/(r1+a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:52:41 2004 Input: (r1 + b) * sin(w3) = x2 - x3 + (r1 + a) * (x1 - x2 + r1 * sin(w1))/(r1 + a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-x ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:53:17 2004 Input: (r1 + b) * sin(w3) = x2 - x3 + (r1 + a) * (x1 - y + r1 * sin(w1))/(r1 + a) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (r1+b)*sin(w3)=x2-x3+(r1+a)*(x1-y ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:53:53 2004 Input: (a + b) * sin(c) = d - e + (a + f) * (g - y + h * sin(c))/(a + f) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (a+b)*sin(c)=d-e+(a+f)*(g-y+h*s ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:11 2004 Input: (a + b) * sin(c) = d - e + (a + f) * (g - y + h * s(c))/(a + f) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (a+b)*sin(c)=d-e+(a+f)*(g-y+h*s ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:22 2004 Input: (a + b) * sin(c) = d - e + (a + f) * (g - y + h * SIN(c))/(a + f) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: (a+b)*sin(c)=d-e+(a+f)*(g-y+h*S ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:28 2004 Input: SIN(1) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SIN(1) ^------ Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:34 2004 Input: sin(1) Output: ? 0.84147098480789650665250232163029899962 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:54:57 2004 Input: sin(a) Output: ? a - 1/6*a^3 + 1/120*a^5 - 1/5040*a^7 + 1/362880*a^9 - 1/39916800*a^11 + 1/6227020800*a^13 - 1/1307674368000*a^15 + O(a^17) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:08 2004 Input: b*sin(a) Output: ? (a - 1/6*a^3 + 1/120*a^5 - 1/5040*a^7 + 1/362880*a^9 - 1/39916800*a^11 + 1/6227020800*a^13 - 1/1307674368000*a^15 + O(a^17))*b ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:32 2004 Input: b1*sin(a) Output: ? (a - 1/6*a^3 + 1/120*a^5 - 1/5040*a^7 + 1/362880*a^9 - 1/39916800*a^11 + 1/6227020800*a^13 - 1/1307674368000*a^15 + O(a^17))*b1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:37 2004 Input: b1*sin(a1) Output: ? (a1 - 1/6*a1^3 + 1/120*a1^5 - 1/5040*a1^7 + 1/362880*a1^9 - 1/39916800*a1^11 + 1/6227020800*a1^13 - 1/1307674368000*a1^15 + O(a1^17))*b1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:55:42 2004 Input: b1*sin(a1)=c Output: ? ? Errors (if any) and Timing Info: *** unexpected character: b1*sin(a1)=c ^--- Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:03 2004 Input: b1*sin(a1) == c Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.018s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:34 2004 Input: (y2-y1+a*cos(w2))/(cos (w1) - cos (w2)) Output: ? ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 - 1/3*w1^-2 - 11/360 - 31/15120*w1^2 - 41/362880*w1^4 - 31/5702400*w1^6 - 10331/43589145600*w1^8 - 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 - 1/3*w1^-4 - 7/180*w1^-2 - 19/5040 - 557/1814400*w1^2 - 73/3421440*w1^4 - 40409/31135104000*w1^6 - 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (-2*w1^-8 - 1/3*w1^-6 - 7/180*w1^-4 - 31/7560*w1^-2 - 247/604800 - 637/17107200*w1^2 - 396073/130767436800*w1^4 - 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (-2*w1^-10 - 1/3*w1^-8 - 7/180*w1^-6 - 31/7560*w1^-4 - 127/302400*w1^-2 - 1013/23950080 - 2673989/653837184000*w1^2 - 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (-2*w1^-12 - 1/3*w1^-10 - 7/180*w1^-8 - 31/7560*w1^-6 - 127/302400*w1^-4 - 73/1710720*w1^-2 - 940451/217945728000 - 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (-2*w1^-14 - 1/3*w1^-12 - 7/180*w1^-10 - 31/7560*w1^-8 - 127/302400*w1^-6 - 73/1710720*w1^-4 - 1414477/326918592000*w1^-2 - 16369/37362124800 + O(w1^2))*w2^12 + (-2*w1^-16 - 1/3*w1^-14 - 7/180*w1^-12 - 31/7560*w1^-10 - 127/302400*w1^-8 - 73/1710720*w1^-6 - 1414477/326918592000*w1^-4 - 8191/18681062400*w1^-2 + O(1))*w2^14 + (-2*w1^-18 - 1/3*w1^-16 - 7/180*w1^-14 - 31/7560*w1^-12 - 127/302400*w1^-10 - 73/1710720*w1^-8 - 1414477/326918592000*w1^-6 - 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y2 + (((2*w1^-2 + 1/6 + 1/120*w1^2 + 1/3024*w1^4 + 1/86400*w1^6 + 1/2661120*w1^8 + 691/59439744000*w1^10 + 1/2874009600*w1^12 + O(w1^14)) + (2*w1^-4 + 1/3*w1^-2 + 11/360 + 31/15120*w1^2 + 41/362880*w1^4 + 31/5702400*w1^6 + 10331/43589145600*w1^8 + 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (2*w1^-6 + 1/3*w1^-4 + 7/180*w1^-2 + 19/5040 + 557/1814400*w1^2 + 73/3421440*w1^4 + 40409/31135104000*w1^6 + 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (2*w1^-8 + 1/3*w1^-6 + 7/180*w1^-4 + 31/7560*w1^-2 + 247/604800 + 637/17107200*w1^2 + 396073/130767436800*w1^4 + 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (2*w1^-10 + 1/3*w1^-8 + 7/180*w1^-6 + 31/7560*w1^-4 + 127/302400*w1^-2 + 1013/23950080 + 2673989/653837184000*w1^2 + 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (2*w1^-12 + 1/3*w1^-10 + 7/180*w1^-8 + 31/7560*w1^-6 + 127/302400*w1^-4 + 73/1710720*w1^-2 + 940451/217945728000 + 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (2*w1^-14 + 1/3*w1^-12 + 7/180*w1^-10 + 31/7560*w1^-8 + 127/302400*w1^-6 + 73/1710720*w1^-4 + 1414477/326918592000*w1^-2 + 16369/37362124800 + O(w1^2))*w2^12 + (2*w1^-16 + 1/3*w1^-14 + 7/180*w1^-12 + 31/7560*w1^-10 + 127/302400*w1^-8 + 73/1710720*w1^-6 + 1414477/326918592000*w1^-4 + 8191/18681062400*w1^-2 + O(1))*w2^14 + (2*w1^-18 + 1/3*w1^-16 + 7/180*w1^-14 + 31/7560*w1^-12 + 127/302400*w1^-10 + 73/1710720*w1^-8 + 1414477/326918592000*w1^-6 + 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y1 + ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 + 2/3*w1^-2 + 19/360 + 2/945*w1^2 + 19/362880*w1^4 + 1/2851200*w1^6 - 2141/43589145600*w1^8 - 337/89159616000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 + 2/3*w1^-4 + 2/45*w1^-2 + 23/5040 + 673/1814400*w1^2 + 2/93[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:48 2004 Input: Simplify((y2-y1+a*cos(w2))/(cos (w1) - cos (w2))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Simplify((y2-y1+a*co ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:56:57 2004 Input: Simplify((y2-y1+a*cos(w2))/(cos(w1) - cos(w2))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Simplify((y2-y1+a*co ^-------------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 14:57:57 2004 Input: Simplify((y2-y1+a*cos(w2))/(cos(w1) - cos(w2))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: Simplify((y2-y1+a*co ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:01:37 2004 Input: simplify((y2-y1+a*cos(w2))/(cos(w1) - cos(w2))) Output: ? ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 - 1/3*w1^-2 - 11/360 - 31/15120*w1^2 - 41/362880*w1^4 - 31/5702400*w1^6 - 10331/43589145600*w1^8 - 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 - 1/3*w1^-4 - 7/180*w1^-2 - 19/5040 - 557/1814400*w1^2 - 73/3421440*w1^4 - 40409/31135104000*w1^6 - 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (-2*w1^-8 - 1/3*w1^-6 - 7/180*w1^-4 - 31/7560*w1^-2 - 247/604800 - 637/17107200*w1^2 - 396073/130767436800*w1^4 - 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (-2*w1^-10 - 1/3*w1^-8 - 7/180*w1^-6 - 31/7560*w1^-4 - 127/302400*w1^-2 - 1013/23950080 - 2673989/653837184000*w1^2 - 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (-2*w1^-12 - 1/3*w1^-10 - 7/180*w1^-8 - 31/7560*w1^-6 - 127/302400*w1^-4 - 73/1710720*w1^-2 - 940451/217945728000 - 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (-2*w1^-14 - 1/3*w1^-12 - 7/180*w1^-10 - 31/7560*w1^-8 - 127/302400*w1^-6 - 73/1710720*w1^-4 - 1414477/326918592000*w1^-2 - 16369/37362124800 + O(w1^2))*w2^12 + (-2*w1^-16 - 1/3*w1^-14 - 7/180*w1^-12 - 31/7560*w1^-10 - 127/302400*w1^-8 - 73/1710720*w1^-6 - 1414477/326918592000*w1^-4 - 8191/18681062400*w1^-2 + O(1))*w2^14 + (-2*w1^-18 - 1/3*w1^-16 - 7/180*w1^-14 - 31/7560*w1^-12 - 127/302400*w1^-10 - 73/1710720*w1^-8 - 1414477/326918592000*w1^-6 - 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y2 + (((2*w1^-2 + 1/6 + 1/120*w1^2 + 1/3024*w1^4 + 1/86400*w1^6 + 1/2661120*w1^8 + 691/59439744000*w1^10 + 1/2874009600*w1^12 + O(w1^14)) + (2*w1^-4 + 1/3*w1^-2 + 11/360 + 31/15120*w1^2 + 41/362880*w1^4 + 31/5702400*w1^6 + 10331/43589145600*w1^8 + 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (2*w1^-6 + 1/3*w1^-4 + 7/180*w1^-2 + 19/5040 + 557/1814400*w1^2 + 73/3421440*w1^4 + 40409/31135104000*w1^6 + 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (2*w1^-8 + 1/3*w1^-6 + 7/180*w1^-4 + 31/7560*w1^-2 + 247/604800 + 637/17107200*w1^2 + 396073/130767436800*w1^4 + 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (2*w1^-10 + 1/3*w1^-8 + 7/180*w1^-6 + 31/7560*w1^-4 + 127/302400*w1^-2 + 1013/23950080 + 2673989/653837184000*w1^2 + 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (2*w1^-12 + 1/3*w1^-10 + 7/180*w1^-8 + 31/7560*w1^-6 + 127/302400*w1^-4 + 73/1710720*w1^-2 + 940451/217945728000 + 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (2*w1^-14 + 1/3*w1^-12 + 7/180*w1^-10 + 31/7560*w1^-8 + 127/302400*w1^-6 + 73/1710720*w1^-4 + 1414477/326918592000*w1^-2 + 16369/37362124800 + O(w1^2))*w2^12 + (2*w1^-16 + 1/3*w1^-14 + 7/180*w1^-12 + 31/7560*w1^-10 + 127/302400*w1^-8 + 73/1710720*w1^-6 + 1414477/326918592000*w1^-4 + 8191/18681062400*w1^-2 + O(1))*w2^14 + (2*w1^-18 + 1/3*w1^-16 + 7/180*w1^-14 + 31/7560*w1^-12 + 127/302400*w1^-10 + 73/1710720*w1^-8 + 1414477/326918592000*w1^-6 + 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y1 + ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 + 2/3*w1^-2 + 19/360 + 2/945*w1^2 + 19/362880*w1^4 + 1/2851200*w1^6 - 2141/43589145600*w1^8 - 337/89159616000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 + 2/3*w1^-4 + 2/45*w1^-2 + 23/5040 + 673/1814400*w1^2 + 2/93[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.008s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:04:32 2004 Input: r1:=(y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: r1:=(y2-y1+a*cos(w2))/ ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:04:42 2004 Input: (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 - 1/3*w1^-2 - 11/360 - 31/15120*w1^2 - 41/362880*w1^4 - 31/5702400*w1^6 - 10331/43589145600*w1^8 - 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 - 1/3*w1^-4 - 7/180*w1^-2 - 19/5040 - 557/1814400*w1^2 - 73/3421440*w1^4 - 40409/31135104000*w1^6 - 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (-2*w1^-8 - 1/3*w1^-6 - 7/180*w1^-4 - 31/7560*w1^-2 - 247/604800 - 637/17107200*w1^2 - 396073/130767436800*w1^4 - 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (-2*w1^-10 - 1/3*w1^-8 - 7/180*w1^-6 - 31/7560*w1^-4 - 127/302400*w1^-2 - 1013/23950080 - 2673989/653837184000*w1^2 - 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (-2*w1^-12 - 1/3*w1^-10 - 7/180*w1^-8 - 31/7560*w1^-6 - 127/302400*w1^-4 - 73/1710720*w1^-2 - 940451/217945728000 - 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (-2*w1^-14 - 1/3*w1^-12 - 7/180*w1^-10 - 31/7560*w1^-8 - 127/302400*w1^-6 - 73/1710720*w1^-4 - 1414477/326918592000*w1^-2 - 16369/37362124800 + O(w1^2))*w2^12 + (-2*w1^-16 - 1/3*w1^-14 - 7/180*w1^-12 - 31/7560*w1^-10 - 127/302400*w1^-8 - 73/1710720*w1^-6 - 1414477/326918592000*w1^-4 - 8191/18681062400*w1^-2 + O(1))*w2^14 + (-2*w1^-18 - 1/3*w1^-16 - 7/180*w1^-14 - 31/7560*w1^-12 - 127/302400*w1^-10 - 73/1710720*w1^-8 - 1414477/326918592000*w1^-6 - 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y2 + (((2*w1^-2 + 1/6 + 1/120*w1^2 + 1/3024*w1^4 + 1/86400*w1^6 + 1/2661120*w1^8 + 691/59439744000*w1^10 + 1/2874009600*w1^12 + O(w1^14)) + (2*w1^-4 + 1/3*w1^-2 + 11/360 + 31/15120*w1^2 + 41/362880*w1^4 + 31/5702400*w1^6 + 10331/43589145600*w1^8 + 3421/356638464000*w1^10 + O(w1^12))*w2^2 + (2*w1^-6 + 1/3*w1^-4 + 7/180*w1^-2 + 19/5040 + 557/1814400*w1^2 + 73/3421440*w1^4 + 40409/31135104000*w1^6 + 18521/261534873600*w1^8 + O(w1^10))*w2^4 + (2*w1^-8 + 1/3*w1^-6 + 7/180*w1^-4 + 31/7560*w1^-2 + 247/604800 + 637/17107200*w1^2 + 396073/130767436800*w1^4 + 8191/37362124800*w1^6 + O(w1^8))*w2^6 + (2*w1^-10 + 1/3*w1^-8 + 7/180*w1^-6 + 31/7560*w1^-4 + 127/302400*w1^-2 + 1013/23950080 + 2673989/653837184000*w1^2 + 32051/87178291200*w1^4 + O(w1^6))*w2^8 + (2*w1^-12 + 1/3*w1^-10 + 7/180*w1^-8 + 31/7560*w1^-6 + 127/302400*w1^-4 + 73/1710720*w1^-2 + 940451/217945728000 + 1682479/3923023104000*w1^2 + O(w1^4))*w2^10 + (2*w1^-14 + 1/3*w1^-12 + 7/180*w1^-10 + 31/7560*w1^-8 + 127/302400*w1^-6 + 73/1710720*w1^-4 + 1414477/326918592000*w1^-2 + 16369/37362124800 + O(w1^2))*w2^12 + (2*w1^-16 + 1/3*w1^-14 + 7/180*w1^-12 + 31/7560*w1^-10 + 127/302400*w1^-8 + 73/1710720*w1^-6 + 1414477/326918592000*w1^-4 + 8191/18681062400*w1^-2 + O(1))*w2^14 + (2*w1^-18 + 1/3*w1^-16 + 7/180*w1^-14 + 31/7560*w1^-12 + 127/302400*w1^-10 + 73/1710720*w1^-8 + 1414477/326918592000*w1^-6 + 8191/18681062400*w1^-4 + O(w1^-2))*w2^16 + O(w2^18))*y1 + ((-2*w1^-2 - 1/6 - 1/120*w1^2 - 1/3024*w1^4 - 1/86400*w1^6 - 1/2661120*w1^8 - 691/59439744000*w1^10 - 1/2874009600*w1^12 + O(w1^14)) + (-2*w1^-4 + 2/3*w1^-2 + 19/360 + 2/945*w1^2 + 19/362880*w1^4 + 1/2851200*w1^6 - 2141/43589145600*w1^8 - 337/89159616000*w1^10 + O(w1^12))*w2^2 + (-2*w1^-6 + 2/3*w1^-4 + 2/45*w1^-2 + 23/5040 + 673/1814400*w1^2 + 2/93[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:04:53 2004 Input: r1 := (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: r1:=(y2-y1+a*cos(w2))/ ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:08:10 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:08:38 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) r1(a,b,c,d,e) Output: ? ? ? ((-2*e^-2 - 1/6 - 1/120*e^2 - 1/3024*e^4 - 1/86400*e^6 - 1/2661120*e^8 - 691/59439744000*e^10 - 1/2874009600*e^12 + O(e^14)) + (-2*e^-4 - 1/3*e^-2 - 11/360 - 31/15120*e^2 - 41/362880*e^4 - 31/5702400*e^6 - 10331/43589145600*e^8 - 3421/356638464000*e^10 + O(e^12))*d^2 + (-2*e^-6 - 1/3*e^-4 - 7/180*e^-2 - 19/5040 - 557/1814400*e^2 - 73/3421440*e^4 - 40409/31135104000*e^6 - 18521/261534873600*e^8 + O(e^10))*d^4 + (-2*e^-8 - 1/3*e^-6 - 7/180*e^-4 - 31/7560*e^-2 - 247/604800 - 637/17107200*e^2 - 396073/130767436800*e^4 - 8191/37362124800*e^6 + O(e^8))*d^6 + (-2*e^-10 - 1/3*e^-8 - 7/180*e^-6 - 31/7560*e^-4 - 127/302400*e^-2 - 1013/23950080 - 2673989/653837184000*e^2 - 32051/87178291200*e^4 + O(e^6))*d^8 + (-2*e^-12 - 1/3*e^-10 - 7/180*e^-8 - 31/7560*e^-6 - 127/302400*e^-4 - 73/1710720*e^-2 - 940451/217945728000 - 1682479/3923023104000*e^2 + O(e^4))*d^10 + (-2*e^-14 - 1/3*e^-12 - 7/180*e^-10 - 31/7560*e^-8 - 127/302400*e^-6 - 73/1710720*e^-4 - 1414477/326918592000*e^-2 - 16369/37362124800 + O(e^2))*d^12 + (-2*e^-16 - 1/3*e^-14 - 7/180*e^-12 - 31/7560*e^-10 - 127/302400*e^-8 - 73/1710720*e^-6 - 1414477/326918592000*e^-4 - 8191/18681062400*e^-2 + O(1))*d^14 + (-2*e^-18 - 1/3*e^-16 - 7/180*e^-14 - 31/7560*e^-12 - 127/302400*e^-10 - 73/1710720*e^-8 - 1414477/326918592000*e^-6 - 8191/18681062400*e^-4 + O(e^-2))*d^16 + O(d^18))*a + (((2*e^-2 + 1/6 + 1/120*e^2 + 1/3024*e^4 + 1/86400*e^6 + 1/2661120*e^8 + 691/59439744000*e^10 + 1/2874009600*e^12 + O(e^14)) + (2*e^-4 + 1/3*e^-2 + 11/360 + 31/15120*e^2 + 41/362880*e^4 + 31/5702400*e^6 + 10331/43589145600*e^8 + 3421/356638464000*e^10 + O(e^12))*d^2 + (2*e^-6 + 1/3*e^-4 + 7/180*e^-2 + 19/5040 + 557/1814400*e^2 + 73/3421440*e^4 + 40409/31135104000*e^6 + 18521/261534873600*e^8 + O(e^10))*d^4 + (2*e^-8 + 1/3*e^-6 + 7/180*e^-4 + 31/7560*e^-2 + 247/604800 + 637/17107200*e^2 + 396073/130767436800*e^4 + 8191/37362124800*e^6 + O(e^8))*d^6 + (2*e^-10 + 1/3*e^-8 + 7/180*e^-6 + 31/7560*e^-4 + 127/302400*e^-2 + 1013/23950080 + 2673989/653837184000*e^2 + 32051/87178291200*e^4 + O(e^6))*d^8 + (2*e^-12 + 1/3*e^-10 + 7/180*e^-8 + 31/7560*e^-6 + 127/302400*e^-4 + 73/1710720*e^-2 + 940451/217945728000 + 1682479/3923023104000*e^2 + O(e^4))*d^10 + (2*e^-14 + 1/3*e^-12 + 7/180*e^-10 + 31/7560*e^-8 + 127/302400*e^-6 + 73/1710720*e^-4 + 1414477/326918592000*e^-2 + 16369/37362124800 + O(e^2))*d^12 + (2*e^-16 + 1/3*e^-14 + 7/180*e^-12 + 31/7560*e^-10 + 127/302400*e^-8 + 73/1710720*e^-6 + 1414477/326918592000*e^-4 + 8191/18681062400*e^-2 + O(1))*d^14 + (2*e^-18 + 1/3*e^-16 + 7/180*e^-14 + 31/7560*e^-12 + 127/302400*e^-10 + 73/1710720*e^-8 + 1414477/326918592000*e^-6 + 8191/18681062400*e^-4 + O(e^-2))*d^16 + O(d^18))*b + ((-2*e^-2 - 1/6 - 1/120*e^2 - 1/3024*e^4 - 1/86400*e^6 - 1/2661120*e^8 - 691/59439744000*e^10 - 1/2874009600*e^12 + O(e^14)) + (-2*e^-4 + 2/3*e^-2 + 19/360 + 2/945*e^2 + 19/362880*e^4 + 1/2851200*e^6 - 2141/43589145600*e^8 - 337/89159616000*e^10 + O(e^12))*d^2 + (-2*e^-6 + 2/3*e^-4 + 2/45*e^-2 + 23/5040 + 673/1814400*e^2 + 2/93555*e^4 + 14603/15567552000*e^6 + 8377/261534873600*e^8 + O(e^10))*d^4 + (-2*e^-8 + 2/3*e^-6 + 2/45*e^-4 + 4/945*e^-2 + 263/604800 + 2539/59875200*e^2 + 221701/65383718400*e^4 + 4/1824322[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:09:49 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) (r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a) Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.014s user 0m0.008s sys 0m0.005s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:10:08 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) eval((r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a)) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:10:18 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) (r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a) Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.013s user 0m0.007s sys 0m0.007s ************** PARI ***************** Host 83.129.161.129 (83.129.161.129) Time: Mon Sep 13 15:10:52 2004 Input: r1(y2,y1,a,w2,w1) = (y2-y1+a*cos(w2))/(cos(w1) - cos(w2)) (r1(y2,y1,a,w2,w1)+b)*sin w3 = x2-x3+(r1(y2,y1,a,w2,w1)+a)*(x1-x2+r1*sin w1)/(r1(y2,y1,a,w2,w1)+a) Output: ? ? ? ? Errors (if any) and Timing Info: *** division by zero in gdiv, gdivgs or ginv Timing: real 0m0.013s user 0m0.009s sys 0m0.004s ************** PARI ***************** Host 128.107.253.39 (128.107.253.39) Time: Mon Sep 13 17:14:48 2004 Input: 325313081408936690707937788121346326696346318407751610198083376450388028308079503167465854169242019593646411323750697612266136676131257298464029314111563154373521679078211167496773278289469507571923731919001892792914221553449227182957429438776166026709285933999810647898320217868796698979278618746587154562910827711187655097004006972308335688789576074964131835599898955697005480507583106089134529566926420807971531201031016704211189890531318056269521511979177076114131422338958943833978750550978117932216405193385573662189454415408715189174660163738716326135995592315960060707868657009648863651544009725759647919142454130239393853487875203374883415815706698400328309201178704336183423764127771318306927730196170885845518823351857307078641958018955754407322040205640586952171876261278620244616443229362185583008017815708570427181463511179814453872281076051629125155761396797007479763563179139019708264877402238052580650116995513528190177043215959831673321266282037953976421135501126750855402044046243493902328929017200426032527598348753631131987263625641952627207188158441633692891642272836415001239905309936386434311548836198096504386710841047896184706008478140316065139414896512020348441181503023011522376267877865185790296839968373198872144783317199208834066353452043399939858444211695007112806550701834021848030994544332888949600163606787134127417390253142106975034099834152256449683670956145172630782129708034193270228447783759231817643856915734318454936463390537487293000908776998796343165893282316885152865675750419751312340367916855842390082573709800757101956358053300615366322453623877620567408798800135412694435709304694370763401782712817281764976546924789048940120632012044546225200399890538792777401890111917243072500813725963571173353068036442126358098872919724267290688335774418380774067768626215678175217914308241559258813771671568034447876718295090631345343848457071986450638795543532664654556204228674085922336682194991640092400533681151579151775989970024243891758646855305979543840848832966580897015919454958717312422765554320699488520382171703021034929279093328120215658028423429078841079158705117763645890316526156192385508035403082741886673383528495826008807547974210581957109253766840456798757773552234056859007683707894347686295322255874935239274365114733363148682363081581845713233364149858078547650239045092858460164075155760406711144201363740474719421519242480014360205958320813962179760466909049841731085830759141880403236266584738623506059064423753363797456651060658398480861297121667835031722385992711544954217466420521926253719209040582096855880004296846624392485154780584653016786695198938230820438356661242744161656303174744468863929184672335988327827257425090542873576328955502827566850362206495321451204767556737283761857884032476455871018073070472909826826452713206900763370405932883484426669826883983454244686868309152734631853869495061614175536511518491302440754320907915586224210860795627969648616261770105475388332947066542883395431268346200752186954537222222724972161217509854421051371659112415449461991317140799832759242323056731629565898934957645706875698457392344418421827252120029707194181465135082488002832371009514021615065575808570319073092449984703972879233463899184530319400159457158648185265823208702071598006296037507632281016114771821888547019938469048843519961019299523706516579688912995078387959370413718437887349111623425474573014991992689864236408458231649526094532393144090296107060168720483683747788139641827935620272959132821534132213429723958943472179258791811884422984681572908171490428799099428995233203500337549798787648390962748616930106949412345197109156032279471611915943154461609935373192428467523024241077154018726437559770330296414794593693097462598115989909991587146180028551965232696580791915046399543359917101930569244566340554556705602208423478911930675294241811103880760462949178664644866630941699775087961262445835482337693075145475746673543845591054370050199401815482299546322134244005040571037406575510714756973291502473578854680741999596073299938637044389797214859553164962554130043864257211129788921511975450361920753659982444359367717876226660999482263872008860639385529365252726941284546578543984629362657737474286474387753465051174717436643806782457689590881103501915561217547863704206208061344963418122790629658621167561069062783361472707964846595010426033942589834913271683214757016904260153230295235892044353061732663684372927251064607473611563311458716076973871279015354808480921502011293891218184524945836283918840665303340617882262208710513477032352182125513101626250584942222487220778791496464628016216722210119810961384513005554699974497980850597465005827501884544226842875533871361261325777513712615225320490021275452382904907766095409313831380893086140563828235391827164372946835103378732264821434520478407134916816524129878083863795975169631960679167975600314392540362966547838191365516780619111548996745113262409003659069610268095224396286811859236850899092419890096585096917552354681326828328529973546420177328471735543041036594203258903948920308131621641493969989599979860361282283126667786724203694769144487851426816071235994027051365139183894635691042004882384315086847761309718856090766212121102848723625040021405566566478216762884495896082571118625380594618831144189230855630912040873368061578211006823676321092957490425307291019674505806942428128458843790803147333568531900063044834472090838496745769988044055004798414192297102766130187456706645327014136387425045847725833772284092163687518403096572375036113932225182670447004292141952055327638527268266290150778657257117358988501748236772511525799834680981951927080607118430234587524879061856852597252020731777090064981167959043756094212787191284967069129506268780772230725311403951951483896823176764434032435707140452947082335139667461788105366002668241279680078669643596370471393541754729479635325153680340424719685541943806234990181969556878550811966605312606381855248793748729323840697344962117730138767391747059124015711490148990761367097918895428967599101616486655573024611506883599002049604596241171991755145907194041809672069641870092191320634150526335631244978439823366957592368021636982975510249524102678950234701917757281374965809602099409184267988514120275848433089037584367677904415121428162156088353683002745344484447535746920180546492731507362537294763003672907271167069569563202458475236503321390083316618597868325130900362522928602393397896512856246985064170368355871431548912339910221911189780355425362600174818500805197330312265426990830753027594750268079379682352203631251772788404859152768581227622369844038384510597042652949014520176442164611601405564811146795903941341322636285143774325162203127217611689887767799080906452127898638911245441151988692640956897478310775822118797409298388116183615615178357133203484060725243103678150349618501702364131302389505915456950039261999655988232055501539709318761335748537076000836033403412603034736654622987725515963158604308917325578007402393815818253295053837141478732717680512365945089705002091751726774360099752169221037825971247815024097207425658225223570962717437436969414054755676232533205035043191133361313024217247639773440326414070415175068266880670203235241977603174092952986870615094170178782255986847484523748283731577176776538132007511070979595829011328022552751831906809314654108944034536873669221763961197999730436339298822887268810855798008996980167089904256124597813881361314388891406121641174171382384404814569779986784657884890281049426991826103174131113561925562903392836841624990542037656479841084570864404750540171084150264769509997157596708806265973533619067445688066124868085533172663214007642007619763197315959348033311462332588416520508105476310487235126599170073710016266493315369982721517769627010445811630871842628294110250225191167071370304883170358317557237320946341537570302126082762543352998298419984859117084481460248514887685283131134757071637819282499300248733004333735349942530798290300772000316901737307224628640765069939174245201916701512209226289364648942782834142745490657188705563464304932873526169822468238445668028578148413047966767042721822354191188784826603662826375230123402171456825294922887268535098339296090938420538313400512387150495188478573102251319092430765147666871037835182575546502431979682785947378347479881712787800131378679859431079648826997220918587695145985573512323208197202266669624421204393665810419776263821709004461512675647543840788316205572335227256747892149238802511309604107864391306748947391806292353587602144623383379879722920358447024506997574018411200844889243706507821670062894834916517644112590794236018913407697685523493717373736338779187399272139097066705480424428502188752687993234400317214173275326328909225334139111537250934278953469978088011879992647319740027338288946889835752260094689609066375763409350621255988935511328401742769901540367841111820372739710147855618853962301388794865695959605256843502846464528001608590413439902204778857705376180747225665462327211035459730536969229670581212476647344593090367287911789015682456528100118896769542204597656369128234005973468814997478059010351454836376867682972122060687312317067514102727580590733500429107950091156199045497760844859912560971090552722832357772237940114198119849050024965806640709365226239630974949094524516899969417684801712659124131024678440604531409904168030329418867612975414351521381173549613332283176136129857979663144856917178220410001/1575071 Output: ? 2065386775637013764509268395655474113207254266047382055780871950854202942648804423213085976246416952592273055143232893071271940605415611730925331709564604734475599379826123187442174214936783850200554336401355194736708513796833458193042913232331533160786313340794228627778177732107293569491652241369355124708097779155273985090221373971765943813260329692846429371119771462346811543781728608355652091663972105435066299874932728138675589167290351077948368752768459809837978239323553946672745232125904914332219977343151982749917015902195616509825018451477529115423975124397313268467698643487492713989045634931756396499855905735293163631911673844384687520852753294298024084001157435672318414624659912590016118195282440511224692876396412016211599083590236595095218185120801455630710464869701875309852338271494971229919272310318521686841186912715772519919934250910778784929450144133232595632598017099036857798012929182573869051725258820257564116431678062967785714207689926066675223754999785729376022058981744276304553439287501490615518908980951532546705917546840444825707464352030058917290980996008529147193398328941275880970120306945505976471605667604166318254913449236993539589103580168896185893724810011812307992896052718803090761241673379796035510674231188364423358397507435537444714836421310576556907915273876681419637556302750091580634546676226875660953634808475979654467003926503989024518075414664942918650205025895297864213408689254210239689873762733987578569241580458831970120132851146369548838708111043153945858159730067732263119363615074129293743416708203992721320867778662773718279706907673498955975945212218450434524597968563771178580411377120661639866056354215454034266595042665036847230378126057763601779793494497981821142118202694171712596245099059828782949295109390416626858952862559089552583779564322358644263746258051600586981613346750936610963685415391632157177984084984019454607414799286283948826460703511688821244770521402781794601854018971710810344358889372249833554467419601907113018072410491850189711571446358401065239380029984041916335086937052494998189155240164539983645362167350416845203541333170146906966838486367867769186502723259725349989832385307240173982937748270280876920810343409641843178964962430626041668494359266012048316058487997907645270372667221751582515093488368751080004419799857140075909206918880853372096084276584399758132816639633862342850063536691453021520669994012728186605346102174706607421702000366208274016006800573583705490510737315103874407255677098990971589833865697705257238473647927902641960053994530571978781966276962097936410512902888977020624179993058427313985815235873372187275092114849071322221685084319810750938749252166971062429931254467531137176222249681617951510517344902683442237001104948816668314533328824261706412428839543803592513941995039593538135143957850055182717648182103881315108133596217152317920077857198908338332122923292362317345192108264238400750574390792349351973731787998606972847237150216614968031716323903825205051310209017402848260284837029067587249458039767410243673568625159327796920412201936481377023225985658467940165601375077176976956925243558590020268706204878941983138353823503966583510050077554085327534123[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.025s sys 0m0.008s ************** PARI ***************** Host 64.102.254.33 (64.102.254.33) Time: Mon Sep 13 23:44:52 2004 Input: (2231^1180 + 1)*(2231^4 + 1)/((2231^236 + 1)*(2231^20 + 1)*198241*5952200129551518881) Output: ? 216635795707393167284097542738660076485566469026640083396720239219810006187867841253558311437092699785174312585509398965512294974149220947080033883055800648568674824953102457979045408143225702247411137338328547455750391173100671203810590428057248688800156549914329571663816011952183277134743832568851262612149714731901422248140915130965312742331748026981132126355390827205039913019807022720782258490870075018080069170500528792750473435900472119217957546892893531467117144939344075354628760871332203988230802128136781767476888639473029534622192962037621181751573301118607315197616818092521603699312698702955228195490027563493433690016068480374582985403046776769421825703449822536791606260192458949540177924173569079081064206988286246398797108129167345582140524963079105491917216809614892879175004498154852421041925990069095947939715499101861629064960921794124762096334083521645647350263789416937977930388183514529974402984448477067947864097776301941647382649334705810768027779822415336220507020038072087454801436705989760294539407859060603291657136934507812030921806155844439668279911066460558816736600468951911104892395313005045778802411243331814428427389146949881818624940059760498248969570267130844326894383843060348422772960510901611516022186181146571835153777299181764563174109406371713307492986827419205531324274530755127814459750229732120219233038949710681888327160787919435887724925023085526772218522552003952059321576765846644927672173911374581528722237867859870835139600262896929326159478978831064167088090263293097471024720597372753152971665673234110633870094156723736081687975595914286856545369892016879932386007707891676730611707053918873446588521407823555307014709821366348286401139922575668532142017527908705499914127857482481823398976150246099099747696913630740322683594748834305319348006187011619275876898683317415995019662180097525825600390079952109421738556796114650266634024945379676665548063818433672712222443613088343132854491357088736932417773691911412651681716420522354049264555324111163547653242959995683748344223954532449977165003466994265112427109122168995557803641100307380355954250529410279335007498360037584816525110719493794366419680450223157993690680677490844939710095375904145228104592423371570045422660220152759589714878629209245120371751324460846511668832804394270793460544407490233305901596163759760378327180855921859269675911808016054457758956043709664568531881216402043749739875346975672954346250111575607240614744989129180029374694679789820497851295497195854211215556662657882288190876171780846552910483600209418151030896069758500111312797041898872186502278327299130239852846723670200544346212363630098661799643282312555408979966654119515660372246825562848328641637335997450886848186842968859845149913838038658226188745287964492105064158037199798968206188959128513367393195529982493507765372046592821254993112298567112427128605104210736227808384431614313658369870392816429610701147469523762456266952165435304145273157257327023199755255159690232412723843752485465347862266700142247412131658752734465374601493681967105656767871067443087938815420801 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.007s sys 0m0.005s ************** PARI ***************** Host 217.255.22.3 (217.255.22.3) Time: Tue Sep 14 19:42:44 2004 Input: vector(x^2,x,1,10) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: vector(x^2,x,1,10) ^---- Timing: real 0m0.182s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 217.255.22.3 (217.255.22.3) Time: Tue Sep 14 19:54:50 2004 Input: a(n)=if(n<=0,n==0,2*(issquare(n)-issquare(2*n)+2*sum(i=1,sqrtint(n2),issquare(n-2*i^2)))) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.001s sys 0m0.008s ************** PARI ***************** Host 203.160.1.69 (203.160.1.69) Time: Tue Sep 14 23:25:22 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 203.160.1.69 (203.160.1.69) Time: Tue Sep 14 23:25:23 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 203.160.1.69 (203.160.1.69) Time: Tue Sep 14 23:25:34 2004 Input: 12 Output: ? 12 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 202.154.65.186 (202.154.65.186) Time: Wed Sep 15 00:26:15 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 193.13.42.18 (193.13.42.18) Time: Wed Sep 15 04:50:58 2004 Input: 5*34 Output: ? 170 ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.007s sys 0m0.005s ************** PARI ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 06:57:53 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" AutomorphismGroup(ExtraSpecialGroup(2,3)); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: AutomorphismGroup( *** ExtraSpecialGroup(2, ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 147.188.56.215 (147.188.56.215) Time: Wed Sep 15 07:02:49 2004 Input: E:=ExtraSpecialGroup(2,3); A:=AutomorphismGroup(E); Output: ? ? ? Errors (if any) and Timing Info: *** unexpected character: E:=ExtraSpecialGroup( ^-------------------- *** unexpected character: A:=AutomorphismGroup( ^-------------------- Timing: real 0m0.018s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:45:41 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:46:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:46:42 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?l Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? Errors (if any) and Timing Info: *** l: unknown identifier. Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:46:57 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?igcd Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? Errors (if any) and Timing Info: *** igcd: unknown identifier. Timing: real 0m0.009s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:47:11 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?gcd Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? gcd(x,{y},{flag=0}): greatest common divisor of x and y. flag is optional, and can be 0: default, 1: use the modular gcd algorithm (x and y must be polynomials), 2 use the subresultant algorithm (x and y must be polynomials) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:51:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?gcd a=x-1; b=x^3+2*x+x+1; g=a*b; h=subs(g,x=x^3); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? gcd(x,{y},{flag=0}): greatest common divisor of x and y. flag is optional, and can be 0: default, 1: use the modular gcd algorithm (x and y must be polynomials), 2 use the subresultant algorithm (x and y must be polynomials) ? ? ? ? ? Errors (if any) and Timing Info: *** expected character: '=' instead of: h=subs(g,x=x^3); ^- Timing: real 0m0.028s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:52:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?subs Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? Errors (if any) and Timing Info: *** subs: unknown identifier. Timing: real 0m0.009s user 0m0.007s sys 0m0.001s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:53:05 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" ?subst Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? subst(x,y,z): in expression x, replace the variable y by the expression z. ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:57:47 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" a=x-1; b=x^3+2*x+x+1; g=a*b; h=subst(g,x,x^3); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 212.217.53.101 (212.217.53.101) Time: Wed Sep 15 07:58:00 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" a=x-1; b=x^3+2*x+x+1; g=a*b; h=subst(g,x,x^3); Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? ? ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 134.157.158.46 (134.157.158.46) Time: Wed Sep 15 10:03:07 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 12.47.104.34 (12.47.104.34) Time: Wed Sep 15 13:49:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.169s user 0m0.006s sys 0m0.007s ************** PARI ***************** Host 12.47.104.34 (12.47.104.34) Time: Wed Sep 15 13:49:31 2004 Input: isprime (1, 2) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 134.129.67.107 (134.129.67.107) Time: Wed Sep 15 14:30:08 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:47:30 2004 Input: mod(2,5) Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2,5) ^-------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.023s user 0m0.002s sys 0m0.008s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:49:10 2004 Input: Mod(2,5) Output: ? Mod(2, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:52:35 2004 Input: Mod(2,1) Output: ? Mod(0, 1) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:53:10 2004 Input: Mod(2,1) Output: ? Mod(0, 1) ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:53:16 2004 Input: Mod(2,7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 15:53:17 2004 Input: Mod(2,7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:44:43 2004 Input: Mod(5,2927)^709 Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:47:28 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,4)==Mod(1,4),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:50:30 2004 Input: vector(200,n,if(isprime(n)==3,if(Mod(n,4)==Mod(3,4),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 16:50:45 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,4)==Mod(3,4),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:17:21 2004 Input: isprime(1,100) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in gisprime. Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:18:23 2004 Input: vector(n=1,100,isprime(n)*n) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: vector(n=1,100,isprime(n)*n) ^----------------- Timing: real 0m0.017s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:19:26 2004 Input: vector(n=1,100,(isprime(n))*n) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: vector(n=1,100,(isprime(n))*n) ^------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 137.99.17.151 (137.99.17.151) Time: Wed Sep 15 17:20:10 2004 Input: vector(n=100,n,(isprime(n))*n) Output: ? [0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 29, 0, 31, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:27:02 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(1,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:28:55 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(3,8),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:31:15 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(5,8),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:33:22 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,8)==Mod(7,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.009s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:39:43 2004 Input: issquare(Mod(-1,p)) Output: ? ? Errors (if any) and Timing Info: *** incorrect type in issquare. Timing: real 0m0.009s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:40:34 2004 Input: vector(200,n,if(isprime(n)==1,if(issquare(Mod(-1,n))==1,n,0),0)) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:40:50 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(-1,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.008s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:43:29 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(-2,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 11, 17, 19, 41, 43, 59, 67, 73, 83, 89, 97, 107, 113, 131, 137, 139, 163, 179, 193] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:47:19 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(2,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 7, 17, 23, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:50:41 2004 Input: vecsort(vector(200,n,if(isprime(n)==1,if(issquare(Mod(3,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 131, 157, 167, 179, 181, 191, 193] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:54:05 2004 Input: vecsort(vector(700,n,if(isprime(n)==1,if(issquare(Mod(3,n))==1,n,0),0))) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 11, 13, 23, 37, 47, 59, 61, 71, 73, 83, 97, 107, 109, 131, 157, 167, 179, 181, 191, 193, 227, 229, 239, 241, 251, 263, 277, 311, 313, 337, 347, 349, 359, 373, 383, 397, 409, 419, 421, 431, 433, 443, 457, 467, 479, 491, 503, 541, 563, 577, 587, 599, 601, 613, 647, 659, 661, 673, 683] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 18:54:42 2004 Input: vecsort(vector(500000,n,if(isprime(n)==1,if(issquare(Mod(3,n))==1,n,0),0))) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m3.815s user 0m3.803s sys 0m0.011s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:07 2004 Input: isprime(17) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:22 2004 Input: isprime(37) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:25 2004 Input: isprime(37) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:29 2004 Input: isprime(36) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:44 2004 Input: isprime(29) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:25:52 2004 Input: isprime(53) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:11 2004 Input: isprime(41) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:19 2004 Input: isprime(97) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:33 2004 Input: isprime(61) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:41 2004 Input: isprime(89) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:26:58 2004 Input: isprime(117) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s ************** PARI ***************** Host 137.99.178.250 (137.99.178.250) Time: Wed Sep 15 19:27:16 2004 Input: isprime(113) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 202.154.65.186 (202.154.65.186) Time: Wed Sep 15 22:02:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s ************** PARI ***************** Host 202.154.65.186 (202.154.65.186) Time: Wed Sep 15 22:03:31 2004 Input: /p 70 exp(Pi*sqrt(-1)) Output: ? ? -1.0000000000000000000000000000000000000 + 0.E-38*I ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m0.028s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 62.2.79.21 (62.2.79.21) Time: Thu Sep 16 10:27:38 2004 Input: 100001100001100001100001100001100001 / 7 Output: ? 100001100001100001100001100001100001/7 ? Errors (if any) and Timing Info: Timing: real 0m0.029s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:52:40 2004 Input: Mod(2,5)^2 Output: ? Mod(4, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:52:47 2004 Input: mod(2,5)^2 Output: ? ? Errors (if any) and Timing Info: *** obsolete function: mod(2,5)^2 ^---------- For full compatibility with GP 1.39, type "default(compatible,3)" (you can also set "compatible = 3" in your GPRC file) New syntax: mod(x,y) ===> Mod(x,y) Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:52:56 2004 Input: 3+88 Output: ? 91 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s ************** PARI ***************** Host 137.99.17.121 (137.99.17.121) Time: Thu Sep 16 10:53:05 2004 Input: Mod(5,2927)^3 Output: ? Mod(125, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 128.196.226.99 (128.196.226.99) Time: Thu Sep 16 11:35:14 2004 Input: {v=[]; print(hello);v } Output: ? hello [] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s ************** PARI ***************** Host 217.255.64.110 (217.255.64.110) Time: Thu Sep 16 16:12:08 2004 Input: lim 3^n Output: ? ? Errors (if any) and Timing Info: *** gpow: need integer exponent if series valuation != 0. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:02:17 2004 Input: Mod(3,4) Output: ? Mod(3, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:02:39 2004 Input: Mod(3,4) Output: ? Mod(3, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:02:52 2004 Input: (Mod(3,4)) Output: ? Mod(3, 4) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:04 2004 Input: Mod(3,1,4) Output: ? ? Errors (if any) and Timing Info: *** invalid flag in Mod. Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:09 2004 Input: Mod(3,1) Output: ? Mod(0, 1) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:26 2004 Input: Mod(3,3) Output: ? Mod(0, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:03:41 2004 Input: Mod(28,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.005s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:04:04 2004 Input: (Mod(5,2927))^709 Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:04:31 2004 Input: (Mod(5,2927))^709 Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:05:54 2004 Input: (Mod(5^709,2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:05:58 2004 Input: (Mod(5^709,2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:05:59 2004 Input: (Mod(5^709,2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s ************** PARI ***************** Host 137.99.17.159 (137.99.17.159) Time: Thu Sep 16 18:06:08 2004 Input: (Mod((5^709),2927)) Output: ? Mod(236, 2927) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s ************** PARI ***************** Host 202.246.252.129 (202.246.252.129) Time: Thu Sep 16 23:48:05 2004 Input: 10000! Output: ? 2846259680917054518906413212119868890148051401702799230794179994274411340003764443772990786757784775815884062142317528830042339940153518739052421161382716174819824199827592418289259787898124253120594659962598670656016157203603239792632873671705574197596209947972034615369811989709261127750048419884541047554464244213657330307670362882580354896746111709736957860367019107151273058728104115864056128116538532596842582599558468814643042558983664931705925171720427659740744613340005419405246230343686915405940406622782824837151203832217864462718382292389963899282722187970245938769380309462733229257055545969002787528224254434802112755901916942542902891690721909708369053987374745248337289952180236328274121704026808676921045155584056717255537201585213282903427998981844931361064038148930449962159999935967089298019033699848440466541923625842494716317896119204123310826865107135451684554093603300960721034694437798234943078062606942230268188522759205702923084312618849760656074258627944882715595683153344053442544664841689458042570946167361318760523498228632645292152942347987060334429073715868849917893258069148316885425195600617237263632397442078692464295601230628872012265295296409150830133663098273380635397290150658182257429547589439976511386554120812578868370423920876448476156900126488927159070630640966162803878404448519164379080718611237062213341541506599184387596102392671327654698616365770662643863802984805195276953619525924093090861447190739076858575593478698172073437209310482547562856777769408156407496227525499338411280928963751699021987049240561753178634693979802461973707904186832993101655415074230839317687836692369484902599960772968429397742753626311982541668153189176323483919082100014717893218422780513518173492190114624687576983537344145601312261522139117875968836736408720793700299203827919803870237207803914031236899760815284030605111670948472222487038919999344207139583698306396223207911562404425080891991431983712044559834404755675948921210149815245454359428541439084356441998422485547853216362403009844285533182925315420655123707970581639346029624769701038874220644153662673371542870078912274934068433644288984710084064160009362393526124803797529334392876439831639031277645072247926785170082666959838952615075900734921519759265919270887320259406638211880198885474826604834225645770574397312225970067193606176351357952982179429079770532728326750148802444352868164502616566283754651900617187344226043891929850607151539003110668472736013581670643786175675743918437647965813610059963868955233464878174614324357322486432679848198145843270303589550842053478849336458248259203328808902578238823326577020524897093704721021424841334246526820680673231421448385407418213962184687010835958294696523563276487047571835161687923506836627174371191572336114307012112076760869785155972184648598591864364171685089962551682091079357023111851817477501080462258552131476489749066075287708289766751495100968232968973200062239288805665803614031128546592908407803397490066495320587316494809388381619865885082738246803489786475711667989042356801830350413387573197263089790943571068779730163391808786847494363353389337358690640584841782806519627582643442925805842221294764940294862267076183298[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.282s user 0m0.274s sys 0m0.007s ************** PARI ***************** Host 202.246.252.129 (202.246.252.129) Time: Thu Sep 16 23:48:39 2004 Input: 100000! Output: ? Errors (if any) and Timing Info:/var/www/cgi-bin/calc/gp: line 4: 8015 Killed /usr/bin/gp -q --emacs Timing: real 0m21.042s user 0m20.989s sys 0m0.012s ************** PARI ***************** Host 62.2.79.21 (62.2.79.21) Time: Fri Sep 17 02:22:51 2004 Input: 111112111112111112111112111112111112 / 7 Output: ? 111112111112111112111112111112111112/7 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s ************** PARI ***************** Host 144.51.64.179 (144.51.64.179) Time: Fri Sep 17 10:06:48 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s ************** PARI ***************** Host 208.59.175.120 (208.59.175.120) Time: Fri Sep 17 11:30:22 2004 Input: 2+2; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Fri Sep 17 22:09:06 2004 Input: print("test") Output: ? test ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '65.96.1' ************** PARI ***************** Host 65.96.160.100 (65.96.160.100) Time: Fri Sep 17 22:09:58 2004 Input: print("test") Output: ? test ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '211.30.' ************** PARI ***************** Host 211.30.187.85 (211.30.187.85) Time: Sat Sep 18 02:05:47 2004 Input: 234*321^45 Output: ? 14519187563252854243456798984676802268540497489860429586839182546659153102649370371736217164580823311320389518633834 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '129.94.' ************** PARI ***************** Host 129.94.6.30 (129.94.6.30) Time: Sat Sep 18 03:59:21 2004 Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311 Output: ? 37249588852282552285743302297396100822355179407163315972232664422849771058311 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.185.' ************** PARI ***************** Host 66.185.84.202 (66.185.84.202) Time: Sat Sep 18 04:19:31 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '211.28.' ************** PARI ***************** Host 211.28.121.5 (211.28.121.5) Time: Sat Sep 18 08:06:59 2004 Input: 13724958885228255228574330229739610082235517940716331597223266442284977105831 Output: ? 13724958885228255228574330229739610082235517940716331597223266442284977105831 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '211.28.' ************** PARI ***************** Host 211.28.121.5 (211.28.121.5) Time: Sat Sep 18 08:07:07 2004 Input: 13724958885228255228574330229739610082235517940716331597223266442284977105831 Output: ? 13724958885228255228574330229739610082235517940716331597223266442284977105831 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '144.137' ************** PARI ***************** Host 144.137.23.49 (144.137.23.49) Time: Sat Sep 18 08:07:37 2004 Input: 37249588852282552285743302297396100822355179407163315972232664422849771058311 Output: ? 37249588852282552285743302297396100822355179407163315972232664422849771058311 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:48:28 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:50:12 2004 Input: prime(3152546242366210213560206523355521600144252221600021436516044530245051102652416651041420302) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment I-->S Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:50:34 2004 Input: prime(12) Output: ? 37 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:55:04 2004 Input: isprime(12) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:55:10 2004 Input: isprime(3152546242366210213560206523355521600144252221600021436516044530245051102652416651041420302) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:57:11 2004 Input: factor(127) Output: ? [127 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:57:18 2004 Input: factor(128) Output: ? [2 7] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 08:58:52 2004 Input: factor(3152546242366210213560206523355521600144252221600021436516044530245051102652416651041420302) Output: ? [2 1] [138937 1] [656311 1] [9208136731 1] [689051894591149 1] [2724458387055134565470788141331979134670860991565018247 1] ? Errors (if any) and Timing Info: Timing: real 0m2.245s user 0m2.239s sys 0m0.006s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 09:00:08 2004 Input: isprime(37249588852282552285743302297396100822355179407163315972232664422849771058311) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '144.136' ************** PARI ***************** Host 144.136.24.92 (144.136.24.92) Time: Sat Sep 18 09:00:21 2004 Input: factor(37249588852282552285743302297396100822355179407163315972232664422849771058311) Output: ? [89954413 1] [5299151939 1] [5302144343 1] [5963856163 1] [4281936962959 1] [4710694442959 1] [122514848197837 1] ? Errors (if any) and Timing Info: Timing: real 0m0.841s user 0m0.819s sys 0m0.022s '80.164.' ************** PARI ***************** Host 80.164.88.73 (80.164.88.73) Time: Sat Sep 18 23:56:35 2004 Input: (2x-4)+(5x-19) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: (2x-4)+(5x-19) ^------------ Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '80.164.' ************** PARI ***************** Host 80.164.88.73 (80.164.88.73) Time: Sat Sep 18 23:56:55 2004 Input: (2*x-4)+(5*x-19) Output: ? 7*x - 23 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '66.159.' ************** PARI ***************** Host 66.159.153.176 (66.159.153.176) Time: Sun Sep 19 21:34:52 2004 Input: vector(49,n,isprime(4*n+1)*(4*n+1)) Output: ? [5, 0, 13, 17, 0, 0, 29, 0, 37, 41, 0, 0, 53, 0, 61, 0, 0, 73, 0, 0, 0, 89, 0, 97, 101, 0, 109, 113, 0, 0, 0, 0, 0, 137, 0, 0, 149, 0, 157, 0, 0, 0, 173, 0, 181, 0, 0, 193, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '24.225.' ************** PARI ***************** Host 24.225.143.141 (24.225.143.141) Time: Tue Sep 21 09:42:29 2004 Input: 16486*6; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.023s user 0m0.001s sys 0m0.007s '24.225.' ************** PARI ***************** Host 24.225.143.141 (24.225.143.141) Time: Tue Sep 21 09:42:57 2004 Input: 16486*6-102400; Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.005s '132.205' ************** PARI ***************** Host 132.205.154.57 (132.205.154.57) Time: Tue Sep 21 13:41:19 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '131.215' ************** PARI ***************** Host 131.215.103.145 (131.215.103.145) Time: Tue Sep 21 14:38:44 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '194.126' ************** PARI ***************** Host 194.126.125.249 (194.126.125.249) Time: Tue Sep 21 17:34:40 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:32:53 2004 Input: Mod(2,7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:33:39 2004 Input: Mod(2, 7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:33:42 2004 Input: Mod(2, 7) Output: ? Mod(2, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:05 2004 Input: 2+3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:23 2004 Input: isprime(7) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:37 2004 Input: Mod(4,8) Output: ? Mod(4, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:34:48 2004 Input: Mod(18,8) Output: ? Mod(2, 8) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:39:05 2004 Input: if(Mod(n,9)==Mod(5,9),n,0) Output: ? ? Errors (if any) and Timing Info: *** forbidden division t_POL % t_INT. Timing: real 0m0.016s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:42:05 2004 Input: vector(200,n,if isprime(n)== 1, if(Mod(n,9) == Mod(5,9),n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...tor(200,n,ifisprime(n)==1 *** ,if(Mod(n,9)==Mod(5, ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:44:20 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,9) == Mod(5,9),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:45:00 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,9) == Mod(5,9),n,0),99)) Output: ? [99, 0, 0, 99, 5, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 23, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 41, 99, 0, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 59, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 99, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 0, 99, 0, 99, 99, 99, 113, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 99, 0, 99, 99, 99, 131, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 99, 99, 99, 99, 149, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 99, 99, 167, 99, 99, 99, 99, 99, 0, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 99, 99, 99, 99, 99, 99, 0, 99, 0, 99, 99, 99, 0, 99, 0, 99] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:51:11 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,9) == Mod(1,4),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 19:51:25 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,4) == Mod(1,4),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:08:57 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,4) == Mod(3,4),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 7, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:15:23 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(1,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:24:04 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(3,8),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:30:39 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(5,8),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:33:46 2004 Input: vector(200,n,if (isprime(n)== 1, if(Mod(n,8) == Mod(7,8),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 0, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:49:15 2004 Input: issquare(4) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:55:46 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(-1,n) == 1,n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: '&' instead of: ...if(issquare(Mod(-1,n)==1, *** n,0),0)) ^-------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 20:56:01 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(-1,n)) == 1,n,0),0)) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 21:07:47 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(2,n)) == 1,n,0),0)) Output: ? [0, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 21:08:03 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(-2,n)) == 1,n,0),0)) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 17, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 67, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 137, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 163, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Sep 21 21:14:06 2004 Input: vector(200,n,if (isprime(n)== 1, if(issquare(Mod(3,n)) == 1,n,0),0)) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 107, 0, 109, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 179, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '69.199.' ************** PARI ***************** Host 69.199.8.11 (69.199.8.11) Time: Tue Sep 21 23:43:27 2004 Input: test Output: ? test ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '130.113' ************** PARI ***************** Host 130.113.128.11 (130.113.128.11) Time: Wed Sep 22 11:32:27 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '198.24.' ************** PARI ***************** Host 198.24.6.134 (198.24.6.134) Time: Wed Sep 22 17:26:56 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:40:16 2004 Input: 43137-2*21063 Output: ? 1011 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:40:22 2004 Input: 2*21063 Output: ? 42126 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:11 2004 Input: 21063/1011 Output: ? 7021/337 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:21 2004 Input: 21063/1011*1.0 Output: ? 20.833827893175074183976261127596439169 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:39 2004 Input: 1011*20 Output: ? 20220 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:41:50 2004 Input: 21063-1011*20 Output: ? 843 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:42:20 2004 Input: 1011-843 Output: ? 168 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:02 2004 Input: 168+5*3 Output: ? 183 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:12 2004 Input: 168*5+3 Output: ? 843 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:44 2004 Input: 163 / 3 Output: ? 163/3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:52 2004 Input: 163 / 3 *1.60 Output: ? 86.933333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:43:57 2004 Input: 163 / 3 *1.0 Output: ? 54.333333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:44:31 2004 Input: 163 - 3 *54 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:45:24 2004 Input: 43137 - 21063*2 - 1011 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:45:39 2004 Input: 21063*2 - 1011*20 + 843 Output: ? 22749 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:45:47 2004 Input: 21063 - 1011*20 - 843 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:02 2004 Input: 1011 - 843 -168 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:13 2004 Input: 843 -168*5-3 Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:26 2004 Input: 168-3*54 Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:46:54 2004 Input: 163/3 Output: ? 163/3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:47:05 2004 Input: 163/3*1.0 Output: ? 54.333333333333333333333333333333333333 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:47:16 2004 Input: 163-3*54 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:57:16 2004 Input: 843 - 168 * 5 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 17:57:35 2004 Input: 168/3 Output: ? 56 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:07:46 2004 Input: 21063 * 256 - 43137 *256 Output: ? -5650944 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:07:55 2004 Input: 21063 * 256 - 43137 *125 Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:10:51 2004 Input: 6*256 Output: ? 1536 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:11:20 2004 Input: 6*125 Output: ? 750 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:25:11 2004 Input: gcd(x^2,x) Output: ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:26:05 2004 Input: gcd(x^4+x, x^3+x+1) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:52:26 2004 Input: x^4+x+ x^3+x+1 Output: ? x^4 + x^3 + 2*x + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 18:53:23 2004 Input: (x^4+x)(x)+ (x^3+x+1)(-x^2-x+1) Output: ? x^4 + x ? Errors (if any) and Timing Info: *** Warning: unused characters: (x)+(x^3+x+1)(-x^2-x+1). Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:04:29 2004 Input: vector(49,n,isprime(4*n+1)*(4*n+1)) Output: ? [5, 0, 13, 17, 0, 0, 29, 0, 37, 41, 0, 0, 53, 0, 61, 0, 0, 73, 0, 0, 0, 89, 0, 97, 101, 0, 109, 113, 0, 0, 0, 0, 0, 137, 0, 0, 149, 0, 157, 0, 0, 0, 173, 0, 181, 0, 0, 193, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:06:09 2004 Input: vector(49,n,isprime(4*n+3)*(4*n+3)) Output: ? [7, 11, 0, 19, 23, 0, 31, 0, 0, 43, 47, 0, 0, 59, 0, 67, 71, 0, 79, 83, 0, 0, 0, 0, 103, 107, 0, 0, 0, 0, 127, 131, 0, 139, 0, 0, 151, 0, 0, 163, 167, 0, 0, 179, 0, 0, 191, 0, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:07:46 2004 Input: vector(49,n,isprime(8*n+1)*(8*n+1)) Output: ? [0, 17, 0, 0, 41, 0, 0, 0, 73, 0, 89, 97, 0, 113, 0, 0, 137, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 0, 233, 241, 0, 257, 0, 0, 281, 0, 0, 0, 313, 0, 0, 337, 0, 353, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:07:58 2004 Input: vector(25,n,isprime(8*n+1)*(8*n+1)) Output: ? [0, 17, 0, 0, 41, 0, 0, 0, 73, 0, 89, 97, 0, 113, 0, 0, 137, 0, 0, 0, 0, 0, 0, 193, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:08:11 2004 Input: vector(24,n,isprime(8*n+1)*(8*n+1)) Output: ? [0, 17, 0, 0, 41, 0, 0, 0, 73, 0, 89, 97, 0, 113, 0, 0, 137, 0, 0, 0, 0, 0, 0, 193] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:11:17 2004 Input: vector(24,n,isprime(8*n+3)*(8*n+3)) Output: ? [11, 19, 0, 0, 43, 0, 59, 67, 0, 83, 0, 0, 107, 0, 0, 131, 139, 0, 0, 163, 0, 179, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:11:49 2004 Input: vector(24,n,isprime(8*n+5)*(8*n+5)) Output: ? [13, 0, 29, 37, 0, 53, 61, 0, 0, 0, 0, 101, 109, 0, 0, 0, 0, 149, 157, 0, 173, 181, 0, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:12:55 2004 Input: vector(24,n,isprime(8*n+7)*(8*n+7)) Output: ? [0, 23, 31, 0, 47, 0, 0, 71, 79, 0, 0, 103, 0, 0, 127, 0, 0, 151, 0, 167, 0, 0, 191, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:13:06 2004 Input: vector(24,n,isprime(8*n+5)*(8*n+5)) Output: ? [13, 0, 29, 37, 0, 53, 61, 0, 0, 0, 0, 101, 109, 0, 0, 0, 0, 149, 157, 0, 173, 181, 0, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:13:53 2004 Input: vector(24,n,isprime(8*n+7)*(8*n+7)) Output: ? [0, 23, 31, 0, 47, 0, 0, 71, 79, 0, 0, 103, 0, 0, 127, 0, 0, 151, 0, 167, 0, 0, 191, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:19:35 2004 Input: vector(200,p,isprime(p)*lift(Mod(-1,p))) Output: ? [0, 1, 2, 0, 4, 0, 6, 0, 0, 0, 10, 0, 12, 0, 0, 0, 16, 0, 18, 0, 0, 0, 22, 0, 0, 0, 0, 0, 28, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 40, 0, 42, 0, 0, 0, 46, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 58, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 70, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 82, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 100, 0, 102, 0, 0, 0, 106, 0, 108, 0, 0, 0, 112, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 126, 0, 0, 0, 130, 0, 0, 0, 0, 0, 136, 0, 138, 0, 0, 0, 0, 0, 0, 0, 0, 0, 148, 0, 150, 0, 0, 0, 0, 0, 156, 0, 0, 0, 0, 0, 162, 0, 0, 0, 166, 0, 0, 0, 0, 0, 172, 0, 0, 0, 0, 0, 178, 0, 180, 0, 0, 0, 0, 0, 0, 0, 0, 0, 190, 0, 192, 0, 0, 0, 196, 0, 198, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:20:13 2004 Input: vector(200,p,isprime(p)*p) Output: ? [0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 0, 0, 23, 0, 0, 0, 0, 0, 29, 0, 31, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 0, 0, 47, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 59, 0, 61, 0, 0, 0, 0, 0, 67, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 83, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 103, 0, 0, 0, 107, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 131, 0, 0, 0, 0, 0, 137, 0, 139, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 151, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 163, 0, 0, 0, 167, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 179, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 197, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:21:47 2004 Input: vector(200,p,isprime(p)*issquare(p)*p) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:21:58 2004 Input: Mod(-1,5) Output: ? Mod(4, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:22:08 2004 Input: lift(Mod(-1,5)) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:22:34 2004 Input: vector(200,n,issquare(lift(Mod(-1,n)))*lift(Mod(-1,))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...t(Mod(-1,n)))*lift(Mod(-1,))) ^---- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:22:41 2004 Input: vector(200,n,issquare(lift(Mod(-1,n)))*lift(Mod(-1,n))) Output: ? [0, 1, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 121, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 144, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 169, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:23:46 2004 Input: vector(200,n,issquare(lift(Mod(-1,n)))*n) Output: ? [1, 2, 0, 0, 5, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 122, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 145, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 170, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:24:00 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(-1,n)))*n) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:25:58 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(2,n)))*n) Output: ? [0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:26:24 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(-2,n)))*n) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:28:26 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(3,n)))*n) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:32:41 2004 Input: vector(200,n,isprime(n)*issquare(lift(Mod(3,n)))*n) Output: ? [0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:33:44 2004 Input: Mod(19,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:33:53 2004 Input: lift(Mod(19,3)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:34:03 2004 Input: lift(Mod(3,19)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:34:09 2004 Input: lift(Mod(3,17)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.001s sys 0m0.009s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:34:16 2004 Input: lift(Mod(3,13)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:37:25 2004 Input: lift(Mod(-1,5)) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:37:48 2004 Input: lift(Mod(3,5)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:13 2004 Input: vector(200,p,lift(Mod(3,p)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...ctor(200,p,lift(Mod(3,p)) ^ Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:21 2004 Input: vector(200,p,lift(Mod(3,p))) Output: ? [0, 1, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:43 2004 Input: vector(200,p,lift(Mod(-1,p))) Output: ? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.008s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:38:53 2004 Input: vector(200,p,lift(Mod(-2,p))) Output: ? [0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:39:03 2004 Input: vector(200,p,lift(Mod(-3,p))) Output: ? [0, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:39:10 2004 Input: vector(200,p,lift(Mod(3,p))) Output: ? [0, 1, 0, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:50:17 2004 Input: 16-3 Output: ? 13 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:50:28 2004 Input: Mod(16,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:50:41 2004 Input: Mod(3,16) Output: ? Mod(3, 16) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:53:19 2004 Input: output(1) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: output(1) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:53:25 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 19:55:30 2004 Input: a=1 p=3 lift(Mod(10^a,p)) Output: ? 1 ? 3 ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:06:48 2004 Input: lift(Mod(10^1,3)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:37 2004 Input: lift(Mod(10^1,7)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:41 2004 Input: lift(Mod(10^2,7)) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:46 2004 Input: lift(Mod(10^3,7)) Output: ? 6 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:50 2004 Input: lift(Mod(10^4,7)) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:53 2004 Input: lift(Mod(10^5,7)) Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:07:56 2004 Input: lift(Mod(10^6,7)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:05 2004 Input: lift(Mod(10^1,7)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:09 2004 Input: lift(Mod(10^2,7)) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:15 2004 Input: lift(Mod(10^1,11)) Output: ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:08:19 2004 Input: lift(Mod(10^2,11)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:19 2004 Input: for(x=1,100) lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(x=1,100) ^- *** forbidden division t_SER % t_INT. Timing: real 0m0.019s user 0m0.004s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:29 2004 Input: for(x=1,100), lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: for(x=1,100), ^-- *** forbidden division t_SER % t_INT. Timing: real 0m0.017s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:40 2004 Input: for(x=1,100,1) lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:10:50 2004 Input: for(x=1,100,1) lift(Mod(10^x,11)) end Output: ? ? ? end ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:00 2004 Input: for(x=1,100,1) lift(Mod(10^x,11)) Output: ? ? ? Errors (if any) and Timing Info: *** forbidden division t_SER % t_INT. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:09 2004 Input: for(x=1,100,1) 10^x Output: ? ? 1 + 2.3025850929940456840179914546843642076*x + 2.6509490552391990052808331942970088458*x^2 + 2.0346785922934761968309911917138105302*x^3 + 1.1712551489122669631782576160326523407*x^4 + 0.53938292919558141019969155571017253478*x^5 + 0.20699584869686809669966601589738494188*x^6 + 0.068089365074437062365404040265376061225*x^7 + 0.019597694626478523696827890871476903106*x^8 + 0.0050139288337754400980709098716421545357*x^9 + 0.0011544997789984348762744932557410281187*x^10 + 0.00024166672554424694181414834840877523750*x^11 + 0.000046371516642572196673822381767030756722*x^12 + 0.0000082134125354393875826732889780792315594*x^13 + 0.0000013508629476223687713847303012234340105*x^14 + 0.00000020736512572488417743337826110640379206*x^15 + 0.000000029842240456309650539215555966289087226*x^16 + O(x^17) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:19 2004 Input: for(x=1,100,1) x Output: ? ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:26 2004 Input: for(x=1,100,1) x^10 Output: ? ? x^10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:45 2004 Input: for(x=1,100,x^10) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:11:52 2004 Input: for(x=1,100,x) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:12:55 2004 Input: for(x=1,100,print(x)) Output: ? 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:13:16 2004 Input: for(x=1,100,print(lift(Mod(10^x,11)))) Output: ? 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 10 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:13:29 2004 Input: for(x=1,100,print(lift(Mod(10^x,7)))) Output: ? 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:13:38 2004 Input: for(x=1,100,print(xlift(Mod(10^x,7)))) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: print(xlift( *** Mod(10^x,7)))) ^-------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:09 2004 Input: for(x=1,100,print(x,lift(Mod(10^x,7))))) Output: ? 13 22 36 44 55 61 73 82 96 104 115 121 133 142 156 164 175 181 193 202 216 224 235 241 253 262 276 284 295 301 313 322 336 344 355 361 373 382 396 404 415 421 433 442 456 464 475 481 493 502 516 524 535 541 553 562 576 584 595 601 613 622 636 644 655 661 673 682 696 704 715 721 733 742 756 764 775 781 793 802 816 824 835 841 853 862 876 884 895 901 913 922 936 944 955 961 973 982 996 1004 ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:20 2004 Input: for(x=1,100,print(lift(Mod(10^x,7)))) Output: ? 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:22 2004 Input: for(x=1,100,print(lift(Mod(10^x,7))) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...,print(lift(Mod(10^x,7))) ^ Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:27 2004 Input: for(x=1,100,print(lift(Mod(10^x,7)))) Output: ? 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 5 1 3 2 6 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:31 2004 Input: for(x=1,100,print(x,lift(Mod(10^x,7)))) Output: ? 13 22 36 44 55 61 73 82 96 104 115 121 133 142 156 164 175 181 193 202 216 224 235 241 253 262 276 284 295 301 313 322 336 344 355 361 373 382 396 404 415 421 433 442 456 464 475 481 493 502 516 524 535 541 553 562 576 584 595 601 613 622 636 644 655 661 673 682 696 704 715 721 733 742 756 764 775 781 793 802 816 824 835 841 853 862 876 884 895 901 913 922 936 944 955 961 973 982 996 1004 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:43 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,7)))) Output: ? 1: 3 2: 2 3: 6 4: 4 5: 5 6: 1 7: 3 8: 2 9: 6 10: 4 11: 5 12: 1 13: 3 14: 2 15: 6 16: 4 17: 5 18: 1 19: 3 20: 2 21: 6 22: 4 23: 5 24: 1 25: 3 26: 2 27: 6 28: 4 29: 5 30: 1 31: 3 32: 2 33: 6 34: 4 35: 5 36: 1 37: 3 38: 2 39: 6 40: 4 41: 5 42: 1 43: 3 44: 2 45: 6 46: 4 47: 5 48: 1 49: 3 50: 2 51: 6 52: 4 53: 5 54: 1 55: 3 56: 2 57: 6 58: 4 59: 5 60: 1 61: 3 62: 2 63: 6 64: 4 65: 5 66: 1 67: 3 68: 2 69: 6 70: 4 71: 5 72: 1 73: 3 74: 2 75: 6 76: 4 77: 5 78: 1 79: 3 80: 2 81: 6 82: 4 83: 5 84: 1 85: 3 86: 2 87: 6 88: 4 89: 5 90: 1 91: 3 92: 2 93: 6 94: 4 95: 5 96: 1 97: 3 98: 2 99: 6 100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:48 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,7)))) Output: ? 1: 32: 23: 64: 45: 56: 17: 38: 29: 610: 411: 512: 113: 314: 215: 616: 417: 518: 119: 320: 221: 622: 423: 524: 125: 326: 227: 628: 429: 530: 131: 332: 233: 634: 435: 536: 137: 338: 239: 640: 441: 542: 143: 344: 245: 646: 447: 548: 149: 350: 251: 652: 453: 554: 155: 356: 257: 658: 459: 560: 161: 362: 263: 664: 465: 566: 167: 368: 269: 670: 471: 572: 173: 374: 275: 676: 477: 578: 179: 380: 281: 682: 483: 584: 185: 386: 287: 688: 489: 590: 191: 392: 293: 694: 495: 596: 197: 398: 299: 6100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:14:56 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,7)))) Output: ? 1: 3 2: 2 3: 6 4: 4 5: 5 6: 1 7: 3 8: 2 9: 6 10: 4 11: 5 12: 1 13: 3 14: 2 15: 6 16: 4 17: 5 18: 1 19: 3 20: 2 21: 6 22: 4 23: 5 24: 1 25: 3 26: 2 27: 6 28: 4 29: 5 30: 1 31: 3 32: 2 33: 6 34: 4 35: 5 36: 1 37: 3 38: 2 39: 6 40: 4 41: 5 42: 1 43: 3 44: 2 45: 6 46: 4 47: 5 48: 1 49: 3 50: 2 51: 6 52: 4 53: 5 54: 1 55: 3 56: 2 57: 6 58: 4 59: 5 60: 1 61: 3 62: 2 63: 6 64: 4 65: 5 66: 1 67: 3 68: 2 69: 6 70: 4 71: 5 72: 1 73: 3 74: 2 75: 6 76: 4 77: 5 78: 1 79: 3 80: 2 81: 6 82: 4 83: 5 84: 1 85: 3 86: 2 87: 6 88: 4 89: 5 90: 1 91: 3 92: 2 93: 6 94: 4 95: 5 96: 1 97: 3 98: 2 99: 6 100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:15:10 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,13)))) Output: ? 1: 10 2: 9 3: 12 4: 3 5: 4 6: 1 7: 10 8: 9 9: 12 10: 3 11: 4 12: 1 13: 10 14: 9 15: 12 16: 3 17: 4 18: 1 19: 10 20: 9 21: 12 22: 3 23: 4 24: 1 25: 10 26: 9 27: 12 28: 3 29: 4 30: 1 31: 10 32: 9 33: 12 34: 3 35: 4 36: 1 37: 10 38: 9 39: 12 40: 3 41: 4 42: 1 43: 10 44: 9 45: 12 46: 3 47: 4 48: 1 49: 10 50: 9 51: 12 52: 3 53: 4 54: 1 55: 10 56: 9 57: 12 58: 3 59: 4 60: 1 61: 10 62: 9 63: 12 64: 3 65: 4 66: 1 67: 10 68: 9 69: 12 70: 3 71: 4 72: 1 73: 10 74: 9 75: 12 76: 3 77: 4 78: 1 79: 10 80: 9 81: 12 82: 3 83: 4 84: 1 85: 10 86: 9 87: 12 88: 3 89: 4 90: 1 91: 10 92: 9 93: 12 94: 3 95: 4 96: 1 97: 10 98: 9 99: 12 100: 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:16:04 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,17)))) Output: ? 1: 10 2: 15 3: 14 4: 4 5: 6 6: 9 7: 5 8: 16 9: 7 10: 2 11: 3 12: 13 13: 11 14: 8 15: 12 16: 1 17: 10 18: 15 19: 14 20: 4 21: 6 22: 9 23: 5 24: 16 25: 7 26: 2 27: 3 28: 13 29: 11 30: 8 31: 12 32: 1 33: 10 34: 15 35: 14 36: 4 37: 6 38: 9 39: 5 40: 16 41: 7 42: 2 43: 3 44: 13 45: 11 46: 8 47: 12 48: 1 49: 10 50: 15 51: 14 52: 4 53: 6 54: 9 55: 5 56: 16 57: 7 58: 2 59: 3 60: 13 61: 11 62: 8 63: 12 64: 1 65: 10 66: 15 67: 14 68: 4 69: 6 70: 9 71: 5 72: 16 73: 7 74: 2 75: 3 76: 13 77: 11 78: 8 79: 12 80: 1 81: 10 82: 15 83: 14 84: 4 85: 6 86: 9 87: 5 88: 16 89: 7 90: 2 91: 3 92: 13 93: 11 94: 8 95: 12 96: 1 97: 10 98: 15 99: 14 100: 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:16:36 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,19)))) Output: ? 1: 10 2: 5 3: 12 4: 6 5: 3 6: 11 7: 15 8: 17 9: 18 10: 9 11: 14 12: 7 13: 13 14: 16 15: 8 16: 4 17: 2 18: 1 19: 10 20: 5 21: 12 22: 6 23: 3 24: 11 25: 15 26: 17 27: 18 28: 9 29: 14 30: 7 31: 13 32: 16 33: 8 34: 4 35: 2 36: 1 37: 10 38: 5 39: 12 40: 6 41: 3 42: 11 43: 15 44: 17 45: 18 46: 9 47: 14 48: 7 49: 13 50: 16 51: 8 52: 4 53: 2 54: 1 55: 10 56: 5 57: 12 58: 6 59: 3 60: 11 61: 15 62: 17 63: 18 64: 9 65: 14 66: 7 67: 13 68: 16 69: 8 70: 4 71: 2 72: 1 73: 10 74: 5 75: 12 76: 6 77: 3 78: 11 79: 15 80: 17 81: 18 82: 9 83: 14 84: 7 85: 13 86: 16 87: 8 88: 4 89: 2 90: 1 91: 10 92: 5 93: 12 94: 6 95: 3 96: 11 97: 15 98: 17 99: 18 100: 9 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:16:46 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,23)))) Output: ? 1: 10 2: 8 3: 11 4: 18 5: 19 6: 6 7: 14 8: 2 9: 20 10: 16 11: 22 12: 13 13: 15 14: 12 15: 5 16: 4 17: 17 18: 9 19: 21 20: 3 21: 7 22: 1 23: 10 24: 8 25: 11 26: 18 27: 19 28: 6 29: 14 30: 2 31: 20 32: 16 33: 22 34: 13 35: 15 36: 12 37: 5 38: 4 39: 17 40: 9 41: 21 42: 3 43: 7 44: 1 45: 10 46: 8 47: 11 48: 18 49: 19 50: 6 51: 14 52: 2 53: 20 54: 16 55: 22 56: 13 57: 15 58: 12 59: 5 60: 4 61: 17 62: 9 63: 21 64: 3 65: 7 66: 1 67: 10 68: 8 69: 11 70: 18 71: 19 72: 6 73: 14 74: 2 75: 20 76: 16 77: 22 78: 13 79: 15 80: 12 81: 5 82: 4 83: 17 84: 9 85: 21 86: 3 87: 7 88: 1 89: 10 90: 8 91: 11 92: 18 93: 19 94: 6 95: 14 96: 2 97: 20 98: 16 99: 22 100: 13 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:17:06 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,29)))) Output: ? 1: 10 2: 13 3: 14 4: 24 5: 8 6: 22 7: 17 8: 25 9: 18 10: 6 11: 2 12: 20 13: 26 14: 28 15: 19 16: 16 17: 15 18: 5 19: 21 20: 7 21: 12 22: 4 23: 11 24: 23 25: 27 26: 9 27: 3 28: 1 29: 10 30: 13 31: 14 32: 24 33: 8 34: 22 35: 17 36: 25 37: 18 38: 6 39: 2 40: 20 41: 26 42: 28 43: 19 44: 16 45: 15 46: 5 47: 21 48: 7 49: 12 50: 4 51: 11 52: 23 53: 27 54: 9 55: 3 56: 1 57: 10 58: 13 59: 14 60: 24 61: 8 62: 22 63: 17 64: 25 65: 18 66: 6 67: 2 68: 20 69: 26 70: 28 71: 19 72: 16 73: 15 74: 5 75: 21 76: 7 77: 12 78: 4 79: 11 80: 23 81: 27 82: 9 83: 3 84: 1 85: 10 86: 13 87: 14 88: 24 89: 8 90: 22 91: 17 92: 25 93: 18 94: 6 95: 2 96: 20 97: 26 98: 28 99: 19 100: 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:17:20 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,31)))) Output: ? 1: 10 2: 7 3: 8 4: 18 5: 25 6: 2 7: 20 8: 14 9: 16 10: 5 11: 19 12: 4 13: 9 14: 28 15: 1 16: 10 17: 7 18: 8 19: 18 20: 25 21: 2 22: 20 23: 14 24: 16 25: 5 26: 19 27: 4 28: 9 29: 28 30: 1 31: 10 32: 7 33: 8 34: 18 35: 25 36: 2 37: 20 38: 14 39: 16 40: 5 41: 19 42: 4 43: 9 44: 28 45: 1 46: 10 47: 7 48: 8 49: 18 50: 25 51: 2 52: 20 53: 14 54: 16 55: 5 56: 19 57: 4 58: 9 59: 28 60: 1 61: 10 62: 7 63: 8 64: 18 65: 25 66: 2 67: 20 68: 14 69: 16 70: 5 71: 19 72: 4 73: 9 74: 28 75: 1 76: 10 77: 7 78: 8 79: 18 80: 25 81: 2 82: 20 83: 14 84: 16 85: 5 86: 19 87: 4 88: 9 89: 28 90: 1 91: 10 92: 7 93: 8 94: 18 95: 25 96: 2 97: 20 98: 14 99: 16 100: 5 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:04 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,37)))) Output: ? 1: 10 2: 26 3: 1 4: 10 5: 26 6: 1 7: 10 8: 26 9: 1 10: 10 11: 26 12: 1 13: 10 14: 26 15: 1 16: 10 17: 26 18: 1 19: 10 20: 26 21: 1 22: 10 23: 26 24: 1 25: 10 26: 26 27: 1 28: 10 29: 26 30: 1 31: 10 32: 26 33: 1 34: 10 35: 26 36: 1 37: 10 38: 26 39: 1 40: 10 41: 26 42: 1 43: 10 44: 26 45: 1 46: 10 47: 26 48: 1 49: 10 50: 26 51: 1 52: 10 53: 26 54: 1 55: 10 56: 26 57: 1 58: 10 59: 26 60: 1 61: 10 62: 26 63: 1 64: 10 65: 26 66: 1 67: 10 68: 26 69: 1 70: 10 71: 26 72: 1 73: 10 74: 26 75: 1 76: 10 77: 26 78: 1 79: 10 80: 26 81: 1 82: 10 83: 26 84: 1 85: 10 86: 26 87: 1 88: 10 89: 26 90: 1 91: 10 92: 26 93: 1 94: 10 95: 26 96: 1 97: 10 98: 26 99: 1 100: 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:14 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,41)))) Output: ? 1: 10 2: 18 3: 16 4: 37 5: 1 6: 10 7: 18 8: 16 9: 37 10: 1 11: 10 12: 18 13: 16 14: 37 15: 1 16: 10 17: 18 18: 16 19: 37 20: 1 21: 10 22: 18 23: 16 24: 37 25: 1 26: 10 27: 18 28: 16 29: 37 30: 1 31: 10 32: 18 33: 16 34: 37 35: 1 36: 10 37: 18 38: 16 39: 37 40: 1 41: 10 42: 18 43: 16 44: 37 45: 1 46: 10 47: 18 48: 16 49: 37 50: 1 51: 10 52: 18 53: 16 54: 37 55: 1 56: 10 57: 18 58: 16 59: 37 60: 1 61: 10 62: 18 63: 16 64: 37 65: 1 66: 10 67: 18 68: 16 69: 37 70: 1 71: 10 72: 18 73: 16 74: 37 75: 1 76: 10 77: 18 78: 16 79: 37 80: 1 81: 10 82: 18 83: 16 84: 37 85: 1 86: 10 87: 18 88: 16 89: 37 90: 1 91: 10 92: 18 93: 16 94: 37 95: 1 96: 10 97: 18 98: 16 99: 37 100: 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:21 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,43)))) Output: ? 1: 10 2: 14 3: 11 4: 24 5: 25 6: 35 7: 6 8: 17 9: 41 10: 23 11: 15 12: 21 13: 38 14: 36 15: 16 16: 31 17: 9 18: 4 19: 40 20: 13 21: 1 22: 10 23: 14 24: 11 25: 24 26: 25 27: 35 28: 6 29: 17 30: 41 31: 23 32: 15 33: 21 34: 38 35: 36 36: 16 37: 31 38: 9 39: 4 40: 40 41: 13 42: 1 43: 10 44: 14 45: 11 46: 24 47: 25 48: 35 49: 6 50: 17 51: 41 52: 23 53: 15 54: 21 55: 38 56: 36 57: 16 58: 31 59: 9 60: 4 61: 40 62: 13 63: 1 64: 10 65: 14 66: 11 67: 24 68: 25 69: 35 70: 6 71: 17 72: 41 73: 23 74: 15 75: 21 76: 38 77: 36 78: 16 79: 31 80: 9 81: 4 82: 40 83: 13 84: 1 85: 10 86: 14 87: 11 88: 24 89: 25 90: 35 91: 6 92: 17 93: 41 94: 23 95: 15 96: 21 97: 38 98: 36 99: 16 100: 31 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:26:35 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,47)))) Output: ? 1: 10 2: 6 3: 13 4: 36 5: 31 6: 28 7: 45 8: 27 9: 35 10: 21 11: 22 12: 32 13: 38 14: 4 15: 40 16: 24 17: 5 18: 3 19: 30 20: 18 21: 39 22: 14 23: 46 24: 37 25: 41 26: 34 27: 11 28: 16 29: 19 30: 2 31: 20 32: 12 33: 26 34: 25 35: 15 36: 9 37: 43 38: 7 39: 23 40: 42 41: 44 42: 17 43: 29 44: 8 45: 33 46: 1 47: 10 48: 6 49: 13 50: 36 51: 31 52: 28 53: 45 54: 27 55: 35 56: 21 57: 22 58: 32 59: 38 60: 4 61: 40 62: 24 63: 5 64: 3 65: 30 66: 18 67: 39 68: 14 69: 46 70: 37 71: 41 72: 34 73: 11 74: 16 75: 19 76: 2 77: 20 78: 12 79: 26 80: 25 81: 15 82: 9 83: 43 84: 7 85: 23 86: 42 87: 44 88: 17 89: 29 90: 8 91: 33 92: 1 93: 10 94: 6 95: 13 96: 36 97: 31 98: 28 99: 45 100: 27 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:07 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,53)))) Output: ? 1: 10 2: 47 3: 46 4: 36 5: 42 6: 49 7: 13 8: 24 9: 28 10: 15 11: 44 12: 16 13: 1 14: 10 15: 47 16: 46 17: 36 18: 42 19: 49 20: 13 21: 24 22: 28 23: 15 24: 44 25: 16 26: 1 27: 10 28: 47 29: 46 30: 36 31: 42 32: 49 33: 13 34: 24 35: 28 36: 15 37: 44 38: 16 39: 1 40: 10 41: 47 42: 46 43: 36 44: 42 45: 49 46: 13 47: 24 48: 28 49: 15 50: 44 51: 16 52: 1 53: 10 54: 47 55: 46 56: 36 57: 42 58: 49 59: 13 60: 24 61: 28 62: 15 63: 44 64: 16 65: 1 66: 10 67: 47 68: 46 69: 36 70: 42 71: 49 72: 13 73: 24 74: 28 75: 15 76: 44 77: 16 78: 1 79: 10 80: 47 81: 46 82: 36 83: 42 84: 49 85: 13 86: 24 87: 28 88: 15 89: 44 90: 16 91: 1 92: 10 93: 47 94: 46 95: 36 96: 42 97: 49 98: 13 99: 24 100: 28 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:24 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,59)))) Output: ? 1: 10 2: 41 3: 56 4: 29 5: 54 6: 9 7: 31 8: 15 9: 32 10: 25 11: 14 12: 22 13: 43 14: 17 15: 52 16: 48 17: 8 18: 21 19: 33 20: 35 21: 55 22: 19 23: 13 24: 12 25: 2 26: 20 27: 23 28: 53 29: 58 30: 49 31: 18 32: 3 33: 30 34: 5 35: 50 36: 28 37: 44 38: 27 39: 34 40: 45 41: 37 42: 16 43: 42 44: 7 45: 11 46: 51 47: 38 48: 26 49: 24 50: 4 51: 40 52: 46 53: 47 54: 57 55: 39 56: 36 57: 6 58: 1 59: 10 60: 41 61: 56 62: 29 63: 54 64: 9 65: 31 66: 15 67: 32 68: 25 69: 14 70: 22 71: 43 72: 17 73: 52 74: 48 75: 8 76: 21 77: 33 78: 35 79: 55 80: 19 81: 13 82: 12 83: 2 84: 20 85: 23 86: 53 87: 58 88: 49 89: 18 90: 3 91: 30 92: 5 93: 50 94: 28 95: 44 96: 27 97: 34 98: 45 99: 37 100: 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:40 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,61)))) Output: ? 1: 10 2: 39 3: 24 4: 57 5: 21 6: 27 7: 26 8: 16 9: 38 10: 14 11: 18 12: 58 13: 31 14: 5 15: 50 16: 12 17: 59 18: 41 19: 44 20: 13 21: 8 22: 19 23: 7 24: 9 25: 29 26: 46 27: 33 28: 25 29: 6 30: 60 31: 51 32: 22 33: 37 34: 4 35: 40 36: 34 37: 35 38: 45 39: 23 40: 47 41: 43 42: 3 43: 30 44: 56 45: 11 46: 49 47: 2 48: 20 49: 17 50: 48 51: 53 52: 42 53: 54 54: 52 55: 32 56: 15 57: 28 58: 36 59: 55 60: 1 61: 10 62: 39 63: 24 64: 57 65: 21 66: 27 67: 26 68: 16 69: 38 70: 14 71: 18 72: 58 73: 31 74: 5 75: 50 76: 12 77: 59 78: 41 79: 44 80: 13 81: 8 82: 19 83: 7 84: 9 85: 29 86: 46 87: 33 88: 25 89: 6 90: 60 91: 51 92: 22 93: 37 94: 4 95: 40 96: 34 97: 35 98: 45 99: 23 100: 47 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:30:58 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,67)))) Output: ? 1: 10 2: 33 3: 62 4: 17 5: 36 6: 25 7: 49 8: 21 9: 9 10: 23 11: 29 12: 22 13: 19 14: 56 15: 24 16: 39 17: 55 18: 14 19: 6 20: 60 21: 64 22: 37 23: 35 24: 15 25: 16 26: 26 27: 59 28: 54 29: 4 30: 40 31: 65 32: 47 33: 1 34: 10 35: 33 36: 62 37: 17 38: 36 39: 25 40: 49 41: 21 42: 9 43: 23 44: 29 45: 22 46: 19 47: 56 48: 24 49: 39 50: 55 51: 14 52: 6 53: 60 54: 64 55: 37 56: 35 57: 15 58: 16 59: 26 60: 59 61: 54 62: 4 63: 40 64: 65 65: 47 66: 1 67: 10 68: 33 69: 62 70: 17 71: 36 72: 25 73: 49 74: 21 75: 9 76: 23 77: 29 78: 22 79: 19 80: 56 81: 24 82: 39 83: 55 84: 14 85: 6 86: 60 87: 64 88: 37 89: 35 90: 15 91: 16 92: 26 93: 59 94: 54 95: 4 96: 40 97: 65 98: 47 99: 1 100: 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:31:21 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,71)))) Output: ? 1: 10 2: 29 3: 6 4: 60 5: 32 6: 36 7: 5 8: 50 9: 3 10: 30 11: 16 12: 18 13: 38 14: 25 15: 37 16: 15 17: 8 18: 9 19: 19 20: 48 21: 54 22: 43 23: 4 24: 40 25: 45 26: 24 27: 27 28: 57 29: 2 30: 20 31: 58 32: 12 33: 49 34: 64 35: 1 36: 10 37: 29 38: 6 39: 60 40: 32 41: 36 42: 5 43: 50 44: 3 45: 30 46: 16 47: 18 48: 38 49: 25 50: 37 51: 15 52: 8 53: 9 54: 19 55: 48 56: 54 57: 43 58: 4 59: 40 60: 45 61: 24 62: 27 63: 57 64: 2 65: 20 66: 58 67: 12 68: 49 69: 64 70: 1 71: 10 72: 29 73: 6 74: 60 75: 32 76: 36 77: 5 78: 50 79: 3 80: 30 81: 16 82: 18 83: 38 84: 25 85: 37 86: 15 87: 8 88: 9 89: 19 90: 48 91: 54 92: 43 93: 4 94: 40 95: 45 96: 24 97: 27 98: 57 99: 2 100: 20 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:31:33 2004 Input: for(x=1,100,print(x,": ",lift(Mod(10^x,73)))) Output: ? 1: 10 2: 27 3: 51 4: 72 5: 63 6: 46 7: 22 8: 1 9: 10 10: 27 11: 51 12: 72 13: 63 14: 46 15: 22 16: 1 17: 10 18: 27 19: 51 20: 72 21: 63 22: 46 23: 22 24: 1 25: 10 26: 27 27: 51 28: 72 29: 63 30: 46 31: 22 32: 1 33: 10 34: 27 35: 51 36: 72 37: 63 38: 46 39: 22 40: 1 41: 10 42: 27 43: 51 44: 72 45: 63 46: 46 47: 22 48: 1 49: 10 50: 27 51: 51 52: 72 53: 63 54: 46 55: 22 56: 1 57: 10 58: 27 59: 51 60: 72 61: 63 62: 46 63: 22 64: 1 65: 10 66: 27 67: 51 68: 72 69: 63 70: 46 71: 22 72: 1 73: 10 74: 27 75: 51 76: 72 77: 63 78: 46 79: 22 80: 1 81: 10 82: 27 83: 51 84: 72 85: 63 86: 46 87: 22 88: 1 89: 10 90: 27 91: 51 92: 72 93: 63 94: 46 95: 22 96: 1 97: 10 98: 27 99: 51 100: 72 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:31:51 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,73)," "))) Output: ? ? Errors (if any) and Timing Info: *** variable name expected: ...x,": ",lift(Mod(10^x,73)," "))) ^----------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:32:27 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,73))," ")) Output: ? 1: 10 2: 27 3: 51 4: 72 5: 63 6: 46 7: 22 8: 1 9: 10 10: 27 11: 51 12: 72 13: 63 14: 46 15: 22 16: 1 17: 10 18: 27 19: 51 20: 72 21: 63 22: 46 23: 22 24: 1 25: 10 26: 27 27: 51 28: 72 29: 63 30: 46 31: 22 32: 1 33: 10 34: 27 35: 51 36: 72 37: 63 38: 46 39: 22 40: 1 41: 10 42: 27 43: 51 44: 72 45: 63 46: 46 47: 22 48: 1 49: 10 50: 27 51: 51 52: 72 53: 63 54: 46 55: 22 56: 1 57: 10 58: 27 59: 51 60: 72 61: 63 62: 46 63: 22 64: 1 65: 10 66: 27 67: 51 68: 72 69: 63 70: 46 71: 22 72: 1 73: 10 74: 27 75: 51 76: 72 77: 63 78: 46 79: 22 80: 1 81: 10 82: 27 83: 51 84: 72 85: 63 86: 46 87: 22 88: 1 89: 10 90: 27 91: 51 92: 72 93: 63 94: 46 95: 22 96: 1 97: 10 98: 27 99: 51 100: 72 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:32:42 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,79))," ")) Output: ? 1: 10 2: 21 3: 52 4: 46 5: 65 6: 18 7: 22 8: 62 9: 67 10: 38 11: 64 12: 8 13: 1 14: 10 15: 21 16: 52 17: 46 18: 65 19: 18 20: 22 21: 62 22: 67 23: 38 24: 64 25: 8 26: 1 27: 10 28: 21 29: 52 30: 46 31: 65 32: 18 33: 22 34: 62 35: 67 36: 38 37: 64 38: 8 39: 1 40: 10 41: 21 42: 52 43: 46 44: 65 45: 18 46: 22 47: 62 48: 67 49: 38 50: 64 51: 8 52: 1 53: 10 54: 21 55: 52 56: 46 57: 65 58: 18 59: 22 60: 62 61: 67 62: 38 63: 64 64: 8 65: 1 66: 10 67: 21 68: 52 69: 46 70: 65 71: 18 72: 22 73: 62 74: 67 75: 38 76: 64 77: 8 78: 1 79: 10 80: 21 81: 52 82: 46 83: 65 84: 18 85: 22 86: 62 87: 67 88: 38 89: 64 90: 8 91: 1 92: 10 93: 21 94: 52 95: 46 96: 65 97: 18 98: 22 99: 62 100: 67 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:33:15 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,83))," ")) Output: ? 1: 10 2: 17 3: 4 4: 40 5: 68 6: 16 7: 77 8: 23 9: 64 10: 59 11: 9 12: 7 13: 70 14: 36 15: 28 16: 31 17: 61 18: 29 19: 41 20: 78 21: 33 22: 81 23: 63 24: 49 25: 75 26: 3 27: 30 28: 51 29: 12 30: 37 31: 38 32: 48 33: 65 34: 69 35: 26 36: 11 37: 27 38: 21 39: 44 40: 25 41: 1 42: 10 43: 17 44: 4 45: 40 46: 68 47: 16 48: 77 49: 23 50: 64 51: 59 52: 9 53: 7 54: 70 55: 36 56: 28 57: 31 58: 61 59: 29 60: 41 61: 78 62: 33 63: 81 64: 63 65: 49 66: 75 67: 3 68: 30 69: 51 70: 12 71: 37 72: 38 73: 48 74: 65 75: 69 76: 26 77: 11 78: 27 79: 21 80: 44 81: 25 82: 1 83: 10 84: 17 85: 4 86: 40 87: 68 88: 16 89: 77 90: 23 91: 64 92: 59 93: 9 94: 7 95: 70 96: 36 97: 28 98: 31 99: 61 100: 29 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:33:27 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,89))," ")) Output: ? 1: 10 2: 11 3: 21 4: 32 5: 53 6: 85 7: 49 8: 45 9: 5 10: 50 11: 55 12: 16 13: 71 14: 87 15: 69 16: 67 17: 47 18: 25 19: 72 20: 8 21: 80 22: 88 23: 79 24: 78 25: 68 26: 57 27: 36 28: 4 29: 40 30: 44 31: 84 32: 39 33: 34 34: 73 35: 18 36: 2 37: 20 38: 22 39: 42 40: 64 41: 17 42: 81 43: 9 44: 1 45: 10 46: 11 47: 21 48: 32 49: 53 50: 85 51: 49 52: 45 53: 5 54: 50 55: 55 56: 16 57: 71 58: 87 59: 69 60: 67 61: 47 62: 25 63: 72 64: 8 65: 80 66: 88 67: 79 68: 78 69: 68 70: 57 71: 36 72: 4 73: 40 74: 44 75: 84 76: 39 77: 34 78: 73 79: 18 80: 2 81: 20 82: 22 83: 42 84: 64 85: 17 86: 81 87: 9 88: 1 89: 10 90: 11 91: 21 92: 32 93: 53 94: 85 95: 49 96: 45 97: 5 98: 50 99: 55 100: 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:33:41 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,97))," ")) Output: ? 1: 10 2: 3 3: 30 4: 9 5: 90 6: 27 7: 76 8: 81 9: 34 10: 49 11: 5 12: 50 13: 15 14: 53 15: 45 16: 62 17: 38 18: 89 19: 17 20: 73 21: 51 22: 25 23: 56 24: 75 25: 71 26: 31 27: 19 28: 93 29: 57 30: 85 31: 74 32: 61 33: 28 34: 86 35: 84 36: 64 37: 58 38: 95 39: 77 40: 91 41: 37 42: 79 43: 14 44: 43 45: 42 46: 32 47: 29 48: 96 49: 87 50: 94 51: 67 52: 88 53: 7 54: 70 55: 21 56: 16 57: 63 58: 48 59: 92 60: 47 61: 82 62: 44 63: 52 64: 35 65: 59 66: 8 67: 80 68: 24 69: 46 70: 72 71: 41 72: 22 73: 26 74: 66 75: 78 76: 4 77: 40 78: 12 79: 23 80: 36 81: 69 82: 11 83: 13 84: 33 85: 39 86: 2 87: 20 88: 6 89: 60 90: 18 91: 83 92: 54 93: 55 94: 65 95: 68 96: 1 97: 10 98: 3 99: 30 100: 9 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:34:59 2004 Input: lift(Mod(3,1)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:07 2004 Input: lift(Mod(1,3)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:18 2004 Input: lift(Mod(1,7)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:27 2004 Input: lift(Mod(1,11)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:42 2004 Input: lift(Mod(11,2)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:35:50 2004 Input: lift(Mod(41,5)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Wed Sep 22 20:36:43 2004 Input: for(x=1,100,print1(x,": ",lift(Mod(10^x,73))," ")) Output: ? 1: 10 2: 27 3: 51 4: 72 5: 63 6: 46 7: 22 8: 1 9: 10 10: 27 11: 51 12: 72 13: 63 14: 46 15: 22 16: 1 17: 10 18: 27 19: 51 20: 72 21: 63 22: 46 23: 22 24: 1 25: 10 26: 27 27: 51 28: 72 29: 63 30: 46 31: 22 32: 1 33: 10 34: 27 35: 51 36: 72 37: 63 38: 46 39: 22 40: 1 41: 10 42: 27 43: 51 44: 72 45: 63 46: 46 47: 22 48: 1 49: 10 50: 27 51: 51 52: 72 53: 63 54: 46 55: 22 56: 1 57: 10 58: 27 59: 51 60: 72 61: 63 62: 46 63: 22 64: 1 65: 10 66: 27 67: 51 68: 72 69: 63 70: 46 71: 22 72: 1 73: 10 74: 27 75: 51 76: 72 77: 63 78: 46 79: 22 80: 1 81: 10 82: 27 83: 51 84: 72 85: 63 86: 46 87: 22 88: 1 89: 10 90: 27 91: 51 92: 72 93: 63 94: 46 95: 22 96: 1 97: 10 98: 27 99: 51 100: 72 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.008s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:19:50 2004 Input: (x^4+x)*(x)+ (x^3+x+1)*(-x^2-x+1) Output: ? -x^4 - x^2 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:20:28 2004 Input: ((x^4+x)*(x))+ (((x^3+x+1)*(-x^2-x+1)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...)+(((x^3+x+1)*(-x^2-x+1)) ^ Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:20:40 2004 Input: ((x^4+x)*(x))+ ((x^3+x+1)*(-x^2-x+1)) Output: ? -x^4 - x^2 + 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:22:40 2004 Input: bezout((x^3+x+1),(x^4+x)) Output: ? [x^3 - x^2 + 1, -x^2 + x - 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:40:26 2004 Input: (x^3+x+1)*(-x^2-x+1)+(x^4+x)(-x^2+x+1) Output: ? -x^5 - 2*x^2 + x + 1 ? Errors (if any) and Timing Info: *** Warning: unused characters: (-x^2+x+1). Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 21:40:53 2004 Input: bezout((x^3+x+1),(x^4+x)) Output: ? [x^3 - x^2 + 1, -x^2 + x - 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:35:48 2004 Input: primes(100) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:35:57 2004 Input: primes(30) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:36:06 2004 Input: primes(25) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:40:09 2004 Input: vector(100,n,if(isprime(n)==1,if(100,m,Mod(10^m,n)==1),0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(100,m,Mod(10^m,n)==1),0) ^ Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:40:29 2004 Input: vector(100,n,if(isprime(n)==1,if(100,m,Mod(10^m,n)==1),m),0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(100,m,Mod(10^m,n)==1),m),0) ^--- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:41:07 2004 Input: vector(100,n,if(isprime(n)==1,if(100,m,Mod(10^m,n)==1),m)),0) Output: ? [m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m, m] ? Errors (if any) and Timing Info: *** Warning: unused characters: ,0). Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:41:42 2004 Input: Mod(10,2) Output: ? Mod(0, 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '128.250' ************** PARI ***************** Host 128.250.87.84 (128.250.87.84) Time: Wed Sep 22 22:41:54 2004 Input: factor(37249588852282552285743302297396100822355179407163315972232664422849771058311) Output: ? [89954413 1] [5299151939 1] [5302144343 1] [5963856163 1] [4281936962959 1] [4710694442959 1] [122514848197837 1] ? Errors (if any) and Timing Info: Timing: real 0m0.850s user 0m0.818s sys 0m0.024s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:42:02 2004 Input: Mod(10,5) Output: ? Mod(0, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:42:07 2004 Input: Mod(10,3) Output: ? Mod(1, 3) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:42:40 2004 Input: vector(200,n,Mod(10,n)) Output: ? [Mod(0, 1), Mod(0, 2), Mod(1, 3), Mod(2, 4), Mod(0, 5), Mod(4, 6), Mod(3, 7), Mod(2, 8), Mod(1, 9), Mod(0, 10), Mod(10, 11), Mod(10, 12), Mod(10, 13), Mod(10, 14), Mod(10, 15), Mod(10, 16), Mod(10, 17), Mod(10, 18), Mod(10, 19), Mod(10, 20), Mod(10, 21), Mod(10, 22), Mod(10, 23), Mod(10, 24), Mod(10, 25), Mod(10, 26), Mod(10, 27), Mod(10, 28), Mod(10, 29), Mod(10, 30), Mod(10, 31), Mod(10, 32), Mod(10, 33), Mod(10, 34), Mod(10, 35), Mod(10, 36), Mod(10, 37), Mod(10, 38), Mod(10, 39), Mod(10, 40), Mod(10, 41), Mod(10, 42), Mod(10, 43), Mod(10, 44), Mod(10, 45), Mod(10, 46), Mod(10, 47), Mod(10, 48), Mod(10, 49), Mod(10, 50), Mod(10, 51), Mod(10, 52), Mod(10, 53), Mod(10, 54), Mod(10, 55), Mod(10, 56), Mod(10, 57), Mod(10, 58), Mod(10, 59), Mod(10, 60), Mod(10, 61), Mod(10, 62), Mod(10, 63), Mod(10, 64), Mod(10, 65), Mod(10, 66), Mod(10, 67), Mod(10, 68), Mod(10, 69), Mod(10, 70), Mod(10, 71), Mod(10, 72), Mod(10, 73), Mod(10, 74), Mod(10, 75), Mod(10, 76), Mod(10, 77), Mod(10, 78), Mod(10, 79), Mod(10, 80), Mod(10, 81), Mod(10, 82), Mod(10, 83), Mod(10, 84), Mod(10, 85), Mod(10, 86), Mod(10, 87), Mod(10, 88), Mod(10, 89), Mod(10, 90), Mod(10, 91), Mod(10, 92), Mod(10, 93), Mod(10, 94), Mod(10, 95), Mod(10, 96), Mod(10, 97), Mod(10, 98), Mod(10, 99), Mod(10, 100), Mod(10, 101), Mod(10, 102), Mod(10, 103), Mod(10, 104), Mod(10, 105), Mod(10, 106), Mod(10, 107), Mod(10, 108), Mod(10, 109), Mod(10, 110), Mod(10, 111), Mod(10, 112), Mod(10, 113), Mod(10, 114), Mod(10, 115), Mod(10, 116), Mod(10, 117), Mod(10, 118), Mod(10, 119), Mod(10, 120), Mod(10, 121), Mod(10, 122), Mod(10, 123), Mod(10, 124), Mod(10, 125), Mod(10, 126), Mod(10, 127), Mod(10, 128), Mod(10, 129), Mod(10, 130), Mod(10, 131), Mod(10, 132), Mod(10, 133), Mod(10, 134), Mod(10, 135), Mod(10, 136), Mod(10, 137), Mod(10, 138), Mod(10, 139), Mod(10, 140), Mod(10, 141), Mod(10, 142), Mod(10, 143), Mod(10, 144), Mod(10, 145), Mod(10, 146), Mod(10, 147), Mod(10, 148), Mod(10, 149), Mod(10, 150), Mod(10, 151), Mod(10, 152), Mod(10, 153), Mod(10, 154), Mod(10, 155), Mod(10, 156), Mod(10, 157), Mod(10, 158), Mod(10, 159), Mod(10, 160), Mod(10, 161), Mod(10, 162), Mod(10, 163), Mod(10, 164), Mod(10, 165), Mod(10, 166), Mod(10, 167), Mod(10, 168), Mod(10, 169), Mod(10, 170), Mod(10, 171), Mod(10, 172), Mod(10, 173), Mod(10, 174), Mod(10, 175), Mod(10, 176), Mod(10, 177), Mod(10, 178), Mod(10, 179), Mod(10, 180), Mod(10, 181), Mod(10, 182), Mod(10, 183), Mod(10, 184), Mod(10, 185), Mod(10, 186), Mod(10, 187), Mod(10, 188), Mod(10, 189), Mod(10, 190), Mod(10, 191), Mod(10, 192), Mod(10, 193), Mod(10, 194), Mod(10, 195), Mod(10, 196), Mod(10, 197), Mod(10, 198), Mod(10, 199), Mod(10, 200)] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:10 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(isprime(n)==1,Mod(10,n)) ^ Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:19 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n))) Output: ? [0, Mod(0, 2), Mod(1, 3), 0, Mod(0, 5), 0, Mod(3, 7), 0, 0, 0, Mod(10, 11), 0, Mod(10, 13), 0, 0, 0, Mod(10, 17), 0, Mod(10, 19), 0, 0, 0, Mod(10, 23), 0, 0, 0, 0, 0, Mod(10, 29), 0, Mod(10, 31), 0, 0, 0, 0, 0, Mod(10, 37), 0, 0, 0, Mod(10, 41), 0, Mod(10, 43), 0, 0, 0, Mod(10, 47), 0, 0, 0, 0, 0, Mod(10, 53), 0, 0, 0, 0, 0, Mod(10, 59), 0, Mod(10, 61), 0, 0, 0, 0, 0, Mod(10, 67), 0, 0, 0, Mod(10, 71), 0, Mod(10, 73), 0, 0, 0, 0, 0, Mod(10, 79), 0, 0, 0, Mod(10, 83), 0, 0, 0, 0, 0, Mod(10, 89), 0, 0, 0, 0, 0, 0, 0, Mod(10, 97), 0, 0, 0, Mod(10, 101), 0, Mod(10, 103), 0, 0, 0, Mod(10, 107), 0, Mod(10, 109), 0, 0, 0, Mod(10, 113), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, Mod(10, 127), 0, 0, 0, Mod(10, 131), 0, 0, 0, 0, 0, Mod(10, 137), 0, Mod(10, 139), 0, 0, 0, 0, 0, 0, 0, 0, 0, Mod(10, 149), 0, Mod(10, 151), 0, 0, 0, 0, 0, Mod(10, 157), 0, 0, 0, 0, 0, Mod(10, 163), 0, 0, 0, Mod(10, 167), 0, 0, 0, 0, 0, Mod(10, 173), 0, 0, 0, 0, 0, Mod(10, 179), 0, Mod(10, 181), 0, 0, 0, 0, 0, 0, 0, 0, 0, Mod(10, 191), 0, Mod(10, 193), 0, 0, 0, Mod(10, 197), 0, Mod(10, 199), 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:32 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n)),2) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...(isprime(n)==1,Mod(10,n)),2) ^--- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:43:40 2004 Input: vector(200,n,if(isprime(n)==1, Mod(10,n),2)) Output: ? [2, Mod(0, 2), Mod(1, 3), 2, Mod(0, 5), 2, Mod(3, 7), 2, 2, 2, Mod(10, 11), 2, Mod(10, 13), 2, 2, 2, Mod(10, 17), 2, Mod(10, 19), 2, 2, 2, Mod(10, 23), 2, 2, 2, 2, 2, Mod(10, 29), 2, Mod(10, 31), 2, 2, 2, 2, 2, Mod(10, 37), 2, 2, 2, Mod(10, 41), 2, Mod(10, 43), 2, 2, 2, Mod(10, 47), 2, 2, 2, 2, 2, Mod(10, 53), 2, 2, 2, 2, 2, Mod(10, 59), 2, Mod(10, 61), 2, 2, 2, 2, 2, Mod(10, 67), 2, 2, 2, Mod(10, 71), 2, Mod(10, 73), 2, 2, 2, 2, 2, Mod(10, 79), 2, 2, 2, Mod(10, 83), 2, 2, 2, 2, 2, Mod(10, 89), 2, 2, 2, 2, 2, 2, 2, Mod(10, 97), 2, 2, 2, Mod(10, 101), 2, Mod(10, 103), 2, 2, 2, Mod(10, 107), 2, Mod(10, 109), 2, 2, 2, Mod(10, 113), 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, Mod(10, 127), 2, 2, 2, Mod(10, 131), 2, 2, 2, 2, 2, Mod(10, 137), 2, Mod(10, 139), 2, 2, 2, 2, 2, 2, 2, 2, 2, Mod(10, 149), 2, Mod(10, 151), 2, 2, 2, 2, 2, Mod(10, 157), 2, 2, 2, 2, 2, Mod(10, 163), 2, 2, 2, Mod(10, 167), 2, 2, 2, 2, 2, Mod(10, 173), 2, 2, 2, 2, 2, Mod(10, 179), 2, Mod(10, 181), 2, 2, 2, 2, 2, 2, 2, 2, 2, Mod(10, 191), 2, Mod(10, 193), 2, 2, 2, Mod(10, 197), 2, Mod(10, 199), 2] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:45:51 2004 Input: vector(200,n,if(isprime(n)==1,ifMod(n,9)==Mod(5,9), n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...=1,ifMod(n,9)==Mod(5,9),n,0),0)) ^------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:46:11 2004 Input: vector(200,n,if(isprime(n)==1,ifMod(n,9)==Mod(5,9),n,0),0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...=1,ifMod(n,9)==Mod(5,9),n,0),0)) ^------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:46:16 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,9)==Mod(5,9),n,0),0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:46:38 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(n,9)==Mod(1,n),n,0),0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:15 2004 Input: vector(200,n,if(isprime(n)==1,if(Mod(10,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:29 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:37 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^2,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:44 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^3,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:47:54 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^4,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:48:00 2004 Input: vector(100,n,if(isprime(n)==1,if(Mod(10^5,n)==Mod(1,n),n,0),0)) Output: ? [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:49:05 2004 Input: vector(100,n,if(Mod(10^n,3)==Mod(1,3),n,0)) Output: ? [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:49:37 2004 Input: vector(100,n,if(Mod(10^n,7)==Mod(1,7),n,0)) Output: ? [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 22:49:50 2004 Input: vector(100,n,if(Mod(10^n,11)==Mod(1,11),n,0)) Output: ? [0, 2, 0, 4, 0, 6, 0, 8, 0, 10, 0, 12, 0, 14, 0, 16, 0, 18, 0, 20, 0, 22, 0, 24, 0, 26, 0, 28, 0, 30, 0, 32, 0, 34, 0, 36, 0, 38, 0, 40, 0, 42, 0, 44, 0, 46, 0, 48, 0, 50, 0, 52, 0, 54, 0, 56, 0, 58, 0, 60, 0, 62, 0, 64, 0, 66, 0, 68, 0, 70, 0, 72, 0, 74, 0, 76, 0, 78, 0, 80, 0, 82, 0, 84, 0, 86, 0, 88, 0, 90, 0, 92, 0, 94, 0, 96, 0, 98, 0, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:00:35 2004 Input: vector(100,n,if(Mod(10^n,3)==Mod(1,3),n,0)) Output: ? [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:00:55 2004 Input: vector(100,n,if(Mod(10^n,7)==Mod(1,7),n,0)) Output: ? [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:01:25 2004 Input: Mod(10^6,7) Output: ? Mod(1, 7) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:01:50 2004 Input: vector(100,n,if(Mod(10^n,11)==Mod(1,11),n,0)) Output: ? [0, 2, 0, 4, 0, 6, 0, 8, 0, 10, 0, 12, 0, 14, 0, 16, 0, 18, 0, 20, 0, 22, 0, 24, 0, 26, 0, 28, 0, 30, 0, 32, 0, 34, 0, 36, 0, 38, 0, 40, 0, 42, 0, 44, 0, 46, 0, 48, 0, 50, 0, 52, 0, 54, 0, 56, 0, 58, 0, 60, 0, 62, 0, 64, 0, 66, 0, 68, 0, 70, 0, 72, 0, 74, 0, 76, 0, 78, 0, 80, 0, 82, 0, 84, 0, 86, 0, 88, 0, 90, 0, 92, 0, 94, 0, 96, 0, 98, 0, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:02:08 2004 Input: vector(100,n,if(Mod(10^n,13)==Mod(1,13),n,0)) Output: ? [0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:02:35 2004 Input: vector(100,n,if(Mod(10^n,17)==Mod(1,17),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:02:54 2004 Input: vector(100,n,if(Mod(10^n,19)==Mod(1,19),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:03:11 2004 Input: vector(100,n,if(Mod(10^n,23)==Mod(1,23),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:03:41 2004 Input: Mod(10^22,23) Output: ? Mod(1, 23) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:04:00 2004 Input: vector(100,n,if(Mod(10^n,29)==Mod(1,29),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:04:32 2004 Input: vector(100,n,if(Mod(10^n,31)==Mod(1,31),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 75, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:04:46 2004 Input: vector(100,n,if(Mod(10^n,37)==Mod(1,37),n,0)) Output: ? [0, 0, 3, 0, 0, 6, 0, 0, 9, 0, 0, 12, 0, 0, 15, 0, 0, 18, 0, 0, 21, 0, 0, 24, 0, 0, 27, 0, 0, 30, 0, 0, 33, 0, 0, 36, 0, 0, 39, 0, 0, 42, 0, 0, 45, 0, 0, 48, 0, 0, 51, 0, 0, 54, 0, 0, 57, 0, 0, 60, 0, 0, 63, 0, 0, 66, 0, 0, 69, 0, 0, 72, 0, 0, 75, 0, 0, 78, 0, 0, 81, 0, 0, 84, 0, 0, 87, 0, 0, 90, 0, 0, 93, 0, 0, 96, 0, 0, 99, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:05:02 2004 Input: vector(100,n,if(Mod(10^n,41)==Mod(1,41),n,0)) Output: ? [0, 0, 0, 0, 5, 0, 0, 0, 0, 10, 0, 0, 0, 0, 15, 0, 0, 0, 0, 20, 0, 0, 0, 0, 25, 0, 0, 0, 0, 30, 0, 0, 0, 0, 35, 0, 0, 0, 0, 40, 0, 0, 0, 0, 45, 0, 0, 0, 0, 50, 0, 0, 0, 0, 55, 0, 0, 0, 0, 60, 0, 0, 0, 0, 65, 0, 0, 0, 0, 70, 0, 0, 0, 0, 75, 0, 0, 0, 0, 80, 0, 0, 0, 0, 85, 0, 0, 0, 0, 90, 0, 0, 0, 0, 95, 0, 0, 0, 0, 100] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:05:14 2004 Input: vector(100,n,if(Mod(10^n,43)==Mod(1,43),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:05:53 2004 Input: Mod(10^5,41) Output: ? Mod(1, 41) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:06:05 2004 Input: Mod(10^21,43) Output: ? Mod(1, 43) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:06:32 2004 Input: vector(100,n,if(Mod(10^n,47)==Mod(1,47),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 92, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:06:56 2004 Input: vector(100,n,if(Mod(10^n,53)==Mod(1,53),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 91, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:07:29 2004 Input: vector(100,n,if(Mod(10^n,59)==Mod(1,59),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:07:40 2004 Input: primes(25) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:08:16 2004 Input: vector(100,n,if(Mod(10^n,61)==Mod(1,61),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:08:42 2004 Input: vector(100,n,if(Mod(10^n,67)==Mod(1,67),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 99, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:09:06 2004 Input: vector(100,n,if(Mod(10^n,71)==Mod(1,71),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:09:30 2004 Input: vector(100,n,if(Mod(10^n,73)==Mod(1,73),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 24, 0, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, 56, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 72, 0, 0, 0, 0, 0, 0, 0, 80, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:09:49 2004 Input: vector(100,n,if(Mod(10^n,79)==Mod(1,79),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 78, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 91, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:10:04 2004 Input: vector(100,n,if(Mod(10^n,83)==Mod(1,83),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:10:29 2004 Input: vector(100,n,if(Mod(10^n,89)==Mod(1,89),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 88, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:10:46 2004 Input: vector(100,n,if(Mod(10^n,89)==Mod(1,97),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Wed Sep 22 23:11:05 2004 Input: vector(100,n,if(Mod(10^n,97)==Mod(1,97),n,0)) Output: ? [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.188.198 (68.118.188.198) Time: Thu Sep 23 02:33:13 2004 Input: vector(200,n,isprime(n)*n*issquare(Mod(-1,n))) Output: ? [0, 2, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 29, 0, 0, 0, 0, 0, 0, 0, 37, 0, 0, 0, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 73, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 101, 0, 0, 0, 0, 0, 0, 0, 109, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 149, 0, 0, 0, 0, 0, 0, 0, 157, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 173, 0, 0, 0, 0, 0, 0, 0, 181, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 193, 0, 0, 0, 197, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.188.198 (68.118.188.198) Time: Thu Sep 23 02:33:45 2004 Input: vector(200,n,isprime(n)*n*issquare(Mod(2,n))) Output: ? [0, 2, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 17, 0, 0, 0, 0, 0, 23, 0, 0, 0, 0, 0, 0, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41, 0, 0, 0, 0, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 71, 0, 73, 0, 0, 0, 0, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 103, 0, 0, 0, 0, 0, 0, 0, 0, 0, 113, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 127, 0, 0, 0, 0, 0, 0, 0, 0, 0, 137, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 151, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 167, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 191, 0, 193, 0, 0, 0, 0, 0, 199, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:05 2004 Input: Mod(3,419) Output: ? Mod(3, 419) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:13 2004 Input: lift(Mod(3,419)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:20 2004 Input: lift(Mod(3,557)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.002s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:26 2004 Input: lift(Mod(3,661)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:44 2004 Input: lift(Mod(3,1)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:47 2004 Input: lift(Mod(3,3)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:51 2004 Input: lift(Mod(3,5)) Output: ? 3 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:54:57 2004 Input: lift(Mod(3,2)) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '69.177.' ************** PARI ***************** Host 69.177.6.111 (69.177.6.111) Time: Thu Sep 23 09:55:11 2004 Input: lift(Mod(3,1)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:36:22 2004 Input: 7+3 x=7+3 Output: ? 10 ? 10 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:36:42 2004 Input: 7+3 x=7+3 x=3 x^3 Output: ? 10 ? 10 ? 3 ? 27 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:37:00 2004 Input: 7+3 x=7+3 x=3 x^3 (x+5)^5 Output: ? 10 ? 10 ? 3 ? 27 ? 32768 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.248.' ************** PARI ***************** Host 68.248.251.86 (68.248.251.86) Time: Thu Sep 23 13:37:17 2004 Input: 7+3 x=7+3 x=3 x^3 (x+5)^5 (y+5)^5 Output: ? 10 ? 10 ? 3 ? 27 ? 32768 ? y^5 + 25*y^4 + 250*y^3 + 1250*y^2 + 3125*y + 3125 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '129.93.' ************** PARI ***************** Host 129.93.181.78 (129.93.181.78) Time: Thu Sep 23 16:55:01 2004 Input: 2 +3 Output: ? 5 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:05:49 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:06:05 2004 Input: 2^160 Output: ? 1461501637330902918203684832716283019655932542976 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:06:20 2004 Input: 2^768 Output: ? 1552518092300708935148979488462502555256886017116696611139052038026050952686376886330878408828646477950487730697131073206171580044114814391444287275041181139204454976020849905550265285631598444825262999193716468750892846853816057856 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:06:49 2004 Input: 2^1024 Output: ? 179769313486231590772930519078902473361797697894230657273430081157732675805500963132708477322407536021120113879871393357658789768814416622492847430639474124377767893424865485276302219601246094119453082952085005768838150682342462881473913110540827237163350510684586298239947245938479716304835356329624224137216 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '82.253.' ************** PARI ***************** Host 82.253.190.110 (82.253.190.110) Time: Fri Sep 24 09:07:03 2004 Input: 2^2048 Output: ? 32317006071311007300714876688669951960444102669715484032130345427524655138867890893197201411522913463688717960921898019494119559150490921095088152386448283120630877367300996091750197750389652106796057638384067568276792218642619756161838094338476170470581645852036305042887575891541065808607552399123930385521914333389668342420684974786564569494856176035326322058077805659331026192708460314150258592864177116725943603718461857357598351152301645904403697613233287231227125684710820209725157101726931323469678542580656697935045997268352998638215525166389437335543602135433229604645318478604952148193555853611059596230656 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:34:49 2004 Input: factor(4323110550526375709294437681284209923347881) Output: ? [471463684608646013689 1] [9169551529965486638129 1] ? Errors (if any) and Timing Info: Timing: real 0m0.753s user 0m0.703s sys 0m0.029s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:35:13 2004 Input: factor(4323110550526375709294437681284209923347881-1) Output: ? [2 3] [5 1] [97 1] [15910439 1] [70029730174991641814638753601159 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.022s sys 0m0.004s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:35:38 2004 Input: factor(4323110550526375709294437681284209923347881) Output: ? [471463684608646013689 1] [9169551529965486638129 1] ? Errors (if any) and Timing Info: Timing: real 0m0.727s user 0m0.708s sys 0m0.019s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:36:06 2004 Input: factor(4323110550526375709294437681284209923347881) Output: ? [471463684608646013689 1] [9169551529965486638129 1] ? Errors (if any) and Timing Info: Timing: real 0m0.733s user 0m0.711s sys 0m0.022s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Sep 24 19:36:15 2004 Input: factor(4323110550526375709294437681284209923347881-1) Output: ? [2 3] [5 1] [97 1] [15910439 1] [70029730174991641814638753601159 1] ? Errors (if any) and Timing Info: Timing: real 0m0.027s user 0m0.022s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Sun Sep 26 00:47:10 2004 Input: SetVerbose("Factorization",true) f := Factorization(35); Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SetVerbose("Factoriz ^-------------------- *** unexpected character: f:=Factorization(35); ^-------------------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Sun Sep 26 00:47:24 2004 Input: SetVerbose("Factorization",true) Factorization(35); Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: SetVerbose("Factoriz ^-------------------- *** unknown function or error in formal parameters: Factorization(35); ^------------------ Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:44:42 2004 Input: 1-365!/365^23*(365-23)! Output: ? -21279115957131455770888363190937546639565804346409980201181533910272215619457419076391037401530210411162516050923706022317037842995049009898940972876530778268329906077799129156407000448076415875526298200295939743790272789687450310994840749315496098408315338198781100420675349981897342078450746710412052607469020723280197652681072126856314506865659925237059778099364310995965400859606052262285593568638785520251747374964246303505021192532263934313673463777907416383851853229478400531095525942124090780356828031533597134773245184764619916121460139973001524443343297351486508976341403318289892184037560893609416113349605339650037390000350448173187881215091218954620267423226023112396503197856446234006644723775458275894412740658910793349662123185323639776306318565577600157297290751623083542516802063863713353699119773456839393988931045804591998629446003495383668290224129829841098205939194885162167357098048113628782890101575205036400852954878268986171459816507036831657257635054059590464156402359509175450620302815962947123217270091644123717952742468313981681054570977196954544356151736485627426058394764425929582917574925286634824457765782061715755996297710531668091984746333873415693834533868394867617916871506563574518165254670015588297473897244407961393792181569265064984970558553522497739404734835410580880438067199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999877954985960253411326304591/122045014039746588673695409 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.005s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:45:10 2004 Input: 1-365!/(365^23)*(365-23)! Output: ? -21279115957131455770888363190937546639565804346409980201181533910272215619457419076391037401530210411162516050923706022317037842995049009898940972876530778268329906077799129156407000448076415875526298200295939743790272789687450310994840749315496098408315338198781100420675349981897342078450746710412052607469020723280197652681072126856314506865659925237059778099364310995965400859606052262285593568638785520251747374964246303505021192532263934313673463777907416383851853229478400531095525942124090780356828031533597134773245184764619916121460139973001524443343297351486508976341403318289892184037560893609416113349605339650037390000350448173187881215091218954620267423226023112396503197856446234006644723775458275894412740658910793349662123185323639776306318565577600157297290751623083542516802063863713353699119773456839393988931045804591998629446003495383668290224129829841098205939194885162167357098048113628782890101575205036400852954878268986171459816507036831657257635054059590464156402359509175450620302815962947123217270091644123717952742468313981681054570977196954544356151736485627426058394764425929582917574925286634824457765782061715755996297710531668091984746333873415693834533868394867617916871506563574518165254670015588297473897244407961393792181569265064984970558553522497739404734835410580880438067199999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999877954985960253411326304591/122045014039746588673695409 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:45:23 2004 Input: 1-(365!/((365^23)*(365-23)!)) Output: ? 38093904702297390785243708291056390518886454060947061/75091883268515350125426207425223147563269805908203125 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '219.167' ************** PARI ***************** Host 219.167.136.209 (219.167.136.209) Time: Sun Sep 26 11:46:12 2004 Input: 1-(365!/((365^36)*(365-36)!)) Output: ? 1020254677714162459167299678915417850742696997256154883555348053744834851444570835157/1225999297380266462740712388357774027978304889870366990534898156352341175079345703125 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 13:41:31 2004 Input: a1(b1,c,wA1)=sqrt((a1(b1,c,wA1)+b1)^2+c^2+2*c*(a1+b1)*cos(wA1)) Output: ? ? Errors (if any) and Timing Info: *** expected character: '(' instead of: ...,c,wA1)+b1)^2+c^2+2*c*(a1 *** +b1)*cos(wA1)) ^-------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 13:42:03 2004 Input: a1(b1,c,wA1)=sqrt((a1(b1,c,wA1)+b1)^2+c^2+2*c*(a1(b1,c,wA1)+b1)*cos(wA1)) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '128.196' ************** PARI ***************** Host 128.196.224.39 (128.196.224.39) Time: Sun Sep 26 14:32:17 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:42:15 2004 Input: simplify(x+x+1+1-x=a) Output: ? 2*x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:42:44 2004 Input: simplify(x+1+1-x=a) Output: ? x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:42:55 2004 Input: simplify(x+1+1-x-a) Output: ? -a + 2 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:43:02 2004 Input: simplify(x+x+1+1-x-a) Output: ? x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:43:09 2004 Input: simplify(x+x+x+1+1-x-a) Output: ? 2*x + (-a + 2) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:43:36 2004 Input: simplify((b2^2-b1^2+2a2b2)^2/(4b1^2)-(b2^2+2a2b2-c^2)^2/(4c^2) - a2^2+(2a2b2+b2^2-c^2)^2/(4c^2) - y^2)^2 - 4y^2(a2^2-(2a2b2+b2^2-c^2)^2/(4c^2)) = 0 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: simplify((b2^2-b1^2+2 *** a2b2)^2/(4b1^2)-(b2^ ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:44:23 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2)) = 0 Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...)-(b2^2+2*a2*b2-c^2)^2/(4 *** c^2)-a2^2+(2*a2*b2+b ^-------------------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:44:53 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4*c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2)) = 0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...a2*b2+b2^2-c^2)^2/(4*c^2))=0 ^--- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:45:05 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4*c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2))=0) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...a2*b2+b2^2-c^2)^2/(4*c^2))=0) ^---- Timing: real 0m0.009s user 0m0.005s sys 0m0.002s '83.129.' ************** PARI ***************** Host 83.129.219.112 (83.129.219.112) Time: Sun Sep 26 16:45:33 2004 Input: simplify((b2^2-b1^2+2*a2*b2)^2/(4*b1^2)-(b2^2+2*a2*b2-c^2)^2/(4*c^2) - a2^2+(2*a2*b2+b2^2-c^2)^2/(4*c^2) - y^2)^2 - 4*y^2*(a2^2-(2*a2*b2+b2^2-c^2)^2/(4*c^2))) Output: ? 1/(16*b1^4)*b2^8 + a2/(2*b1^4)*b2^7 + ((-b1^2 + 6*a2^2)/(4*b1^4))*b2^6 + ((-3*a2*b1^2 + 4*a2^3)/(2*b1^4))*b2^5 + ((((3*c^2 + 8*y^2)/c^2)*b1^4 + (-28*a2^2 - 4*y^2)*b1^2 + 8*a2^4)/(8*b1^4))*b2^4 + ((((3*c^2 + 8*y^2)/c^2)*a2*b1^2 + (-8*a2^3 - 4*y^2*a2))/(2*b1^2))*b2^3 + ((-b1^4 + (((10*c^2 + 16*y^2)/c^2)*a2^2 - 4*y^2)*b1^2 + (-8*a2^4 - 8*y^2*a2^2))/(4*b1^2))*b2^2 + (-1/2*a2*b1^2 + (2*a2^3 - 2*y^2*a2))*b2 + (1/16*b1^4 + (-1/2*a2^2 - 1/2*y^2)*b1^2 + (a2^4 - 2*y^2*a2^2 + (y^2*c^2 + y^4))) ? Errors (if any) and Timing Info: *** Warning: unused characters: ). Timing: real 0m0.009s user 0m0.006s sys 0m0.005s '194.84.' ************** PARI ***************** Host 194.84.45.205 (194.84.45.205) Time: Mon Sep 27 03:42:24 2004 Input: 12345678901234567890123456789012345678901234567890123456789012345678901234567890*11111111112222222221111111111222222222111111111122222222211111111112222222221111111111222222222 Output: ? 137174210027434841989026063200274348418655692742002743484063100138420027434828283950742099999997256652973935651579972578875418256515799727023322072565157997393690009725651580 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '80.141.' ************** PARI ***************** Host 80.141.98.24 (80.141.98.24) Time: Mon Sep 27 16:24:40 2004 Input: 36 = x+y+z Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 36=x+y+z ^------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '80.141.' ************** PARI ***************** Host 80.141.98.24 (80.141.98.24) Time: Mon Sep 27 16:25:03 2004 Input: x+y+z=36 Output: ? x + (y + 36) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:14:47 2004 Input: 932123/11 Output: ? 932123/11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:15:03 2004 Input: 932123/11 Output: ? 932123/11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:15:05 2004 Input: 932123/11 Output: ? 932123/11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:15:11 2004 Input: 932123/11. Output: ? 84738.454545454545454545454545454545455 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '134.71.' ************** PARI ***************** Host 134.71.86.83 (134.71.86.83) Time: Mon Sep 27 17:29:05 2004 Input: precprime(11) Output: ? 11 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Mon Sep 27 22:48:49 2004 Input: NextPrime(Random(2^93))*NextPrime(Random(2^93)) Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: NextPrime( *** Random(2^93))*NextPr ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Mon Sep 27 22:54:38 2004 Input: NextPrime(Random(2^93))*NextPrime(Random(2^93)); Factorization(4878143993485443754165069625209697799685333596237977) Output: ? ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: NextPrime( *** Random(2^93))*NextPr ^-------------------- *** unknown function or error in formal parameters: Factorization(487814 ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:00:50 2004 Input: binomial(-3,7) Output: ? -36 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:01:00 2004 Input: binomial(-3,8) Output: ? 45 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:01:10 2004 Input: binomial(9,-5) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.006s sys 0m0.003s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:05:11 2004 Input: 392+O(6^5) Output: ? 2 + 5*6 + 4*6^2 + 6^3 + O(6^5) ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.006s sys 0m0.003s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:05:23 2004 Input: 2 + 5*6 + 4*6^2 + 6^3 Output: ? 392 ? Errors (if any) and Timing Info: Timing: real 0m0.021s user 0m0.003s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:05:44 2004 Input: 392+O(6^25) Output: ? 2 + 5*6 + 4*6^2 + 6^3 + O(6^25) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:06:46 2004 Input: Mod(1,5) Output: ? Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:07:12 2004 Input: Mod(1,5)*(x^2+1) Output: ? Mod(1, 5)*x^2 + Mod(1, 5) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:07:53 2004 Input: factor(Mod(1,5)*(x^2+1)) Output: ? [Mod(1, 5)*x + Mod(2, 5) 1] [Mod(1, 5)*x + Mod(3, 5) 1] ? Errors (if any) and Timing Info: Timing: real 0m0.044s user 0m0.004s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:08:12 2004 Input: lift(factor(Mod(1,5)*(x^2+1))) Output: ? [x + 2 1] [x + 3 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:23:09 2004 Input: 4^7 Output: ? 16384 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:23:23 2004 Input: 4^7*3 Output: ? 49152 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:23:28 2004 Input: 4^9*3 Output: ? 786432 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:31:29 2004 Input: vector(999,x,if(x=lift(Mod(x^2,10^3)),x,0)) Output: ? [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.012s user 0m0.006s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:33:38 2004 Input: lift(Mod(100^2,10^3)) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.001s sys 0m0.009s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:33:45 2004 Input: lift(Mod(101^2,10^3)) Output: ? 201 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:33:54 2004 Input: lift(Mod(101^2,10^3)) 101^2 Output: ? 201 ? 10201 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:34:02 2004 Input: lift(Mod(102^2,10^3)) 102^2 Output: ? 404 ? 10404 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:35:05 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,x,0)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,x,0)) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:35:24 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:36:52 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0)))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:36:58 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0)))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.008s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:37:09 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:37:23 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print(0))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(0 ^-------------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:37:33 2004 Input: for(x=100,999,if(lift(Mod(x^2,10^3))=x,print(x),print("0"))) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...999,if(lift(Mod(x^2,10^3))=x,print(x),print(" ^-------------------- Timing: real 0m0.009s user 0m0.002s sys 0m0.007s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:41:06 2004 Input: bezout(21,65) Output: ? [31, -10, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:41:29 2004 Input: 21*31+65*-10 Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:47:15 2004 Input: 16*31 Output: ? 496 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:47:41 2004 Input: lift(Mod(496,65)) Output: ? 41 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:48:22 2004 Input: Mod(496,65) Output: ? Mod(41, 65) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:48:34 2004 Input: 21*41 Output: ? 861 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '67.165.' ************** PARI ***************** Host 67.165.21.175 (67.165.21.175) Time: Tue Sep 28 13:48:41 2004 Input: Mod(21*41,65) Output: ? Mod(16, 65) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '216.58.' ************** PARI ***************** Host 216.58.64.34 (216.58.64.34) Time: Tue Sep 28 20:40:37 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:11:27 2004 Input: factorint(32) Output: ? [2 5] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:11:47 2004 Input: factorint(random(2^9)) Output: ? [7 1] [53 1] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.004s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:07 2004 Input: factorint(nextprime(random(2^9))) Output: ? [373 1] ? Errors (if any) and Timing Info: Timing: real 0m0.032s user 0m0.007s sys 0m0.003s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:22 2004 Input: factorint(nextprime(random(2^9))*nextprime(random(2^9)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...))*nextprime(random(2^9)) ^ Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:28 2004 Input: factorint(nextprime(random(2^9))*nextprime(random(2^9))) Output: ? [373 1] [503 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:12:54 2004 Input: factorint(nextprime(random(2^93))*nextprime(random(2^93))) Output: ? [3751220971129886190247702609 1] [7193692355178276170440144247 1] ? Errors (if any) and Timing Info: Timing: real 0m15.398s user 0m15.277s sys 0m0.074s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:15:31 2004 Input: //Factorization(NextPrime(Random(2^93))*NextPrime(Random(2^93))) factorint(nextprime(random(2^93))*nextprime(random(2^93))) Output: ? ? [3751220971129886190247702609 1] [7193692355178276170440144247 1] ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m15.700s user 0m15.607s sys 0m0.091s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:16:45 2004 Input: //Factorization(NextPrime(Random(2^93))*NextPrime(Random(2^93))) factorint(nextprime(random(2^93))*nextprime(random(2^93))) 3751220971129886190247702609*3751220971129886190247702609 Output: ? ? [3751220971129886190247702609 1] [7193692355178276170440144247 1] ? 14071658774244646442417825845321489074333496002505406881 ? Errors (if any) and Timing Info: *** unexpected character: ^- Timing: real 0m15.704s user 0m15.616s sys 0m0.087s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Tue Sep 28 22:30:09 2004 Input: n := NextPrime(Random(2^90))*NextPrime(Random(2^90)); n; Factorization(n); Output: ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: n:=NextPrime(Random(2 ^-------------------- *** expected character: '=' instead of: Factorization(n); ^- Timing: real 0m0.016s user 0m0.005s sys 0m0.004s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:38:29 2004 Input: (a+b)^2; Output: ? ? ? Errors (if any) and Timing Info: Timing: real 0m0.019s user 0m0.005s sys 0m0.003s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:38:37 2004 Input: (a+b)^2 Output: ? a^2 + 2*b*a + b^2 ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:39:13 2004 Input: nf=nfini(x^3+x+1) Output: ? ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: nf=nfini(x^3+x+1) ^------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '134.157' ************** PARI ***************** Host 134.157.86.77 (134.157.86.77) Time: Wed Sep 29 06:39:31 2004 Input: nf=nfinit(x^3+x+1) Output: ? [x^3 + x + 1, [1, 1], -31, 1, [[1, 1.4655712318767680266567312252199391080, -0.68232780382801932736948373971104825689; 1, -0.23278561593838401332836561260996955402 + 0.79255199251544784832589830065336124352*I, 0.34116390191400966368474186985552412844 + 1.1615413999972519360879176872471740748*I], [1, 1.4655712318767680266567312252199391080, -0.68232780382801932736948373971104825689; 1, 0.55976637657706383499753268804339168950, 1.5027053019112615997726595571026982033; 1, -1.0253376084538318616542639132633307975, -0.82037749808324227240317581739164994640], 0, [3, 1, 0; 1, 1, -3; 0, -3, -2], [31, 20, 17; 0, 1, 0; 0, 0, 1], [-11, 2, -3; 2, -6, 9; -3, 9, 2], [31, [14, -1, 10; -11, 3, 1; 1, 11, 14]]], [-0.68232780382801932736948373971104825689, 0.34116390191400966368474186985552412844 + 1.1615413999972519360879176872471740748*I], [1, x^2 + 1, x], [1, 0, -1; 0, 0, 1; 0, 1, 0], [1, 0, 0, 0, 0, -1, 0, -1, -1; 0, 1, 0, 1, 1, 0, 0, 0, 1; 0, 0, 1, 0, -1, 0, 1, 0, 0]] ? ? Errors (if any) and Timing Info: Timing: real 0m0.123s user 0m0.006s sys 0m0.005s '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:48:37 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each evaluated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and evaluating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:49:52 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e.valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e.valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:50:51 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:51:41 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? TheprobabilityofECMfindingafactornearNwithstage1parameterB1 ? stage2parameterB2 ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: srule.Thehconvenientlycancel. *** Warning: unused characters: ,butalpha-1= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? TheprobabilityofECMfindingafactornearNwithstage1parameterB1 ? stage2parameterB2 ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: srule.Thehconvenientlycancel. *** Warning: unused characters: ,butalpha-1= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:54:37 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e-valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e-valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:54:54 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) Boole's rule. The h conveniently cancel for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( Trapezoidal rule. Could be improved sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, redundancy could be avoided by counting how often each gcd(i,S) value occurs n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** Warning: unused characters: srule.Thehconvenientlycancel. *** Warning: unused characters: ,butalpha-1= tablemax, but alpha - 1 < tablemax which would give negative result */ if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, /* dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified */ return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( /* Trapezoidal rule. Could be improved */ sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) /* Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 */ + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each e-valuated at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, /* redundancy could be avoided by counting how often each gcd(i,S) value occurs */ n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and e-valuating nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: WARNING: PARI command contains unsafe command 'eval', so it will not be executed. '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 15:57:14 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) /* Boole's rule. The h conveniently cancel */ for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); /* Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result */ if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, /* dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified */ return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( /* Trapezoidal rule. Could be improved */ sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) /* Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 */ + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, /* redundancy could be avoided by counting how often each gcd(i,S) value occurs */ n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1/ecmprob(1000000,100000000,sqrt(10)*10^34,0,0) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1901.8734260571884364237051189878883491 ? Errors (if any) and Timing Info: Timing: real 0m0.105s user 0m0.087s sys 0m0.005s '141.84.' ************** PARI ***************** Host 141.84.69.18 (141.84.69.18) Time: Wed Sep 29 16:10:06 2004 Input: L2 (x) = { /* int (1 - Log(x-1))/x dx = Log(x) + Log(x)*(Log(1-x) - Log(x-1)) + Dilog(x) Dilog(x) = Pi^2/6 - Log(x)*Log(1-x) - Dilog(1-x) thus: Log(x) - Log(x)*Log(x-1) + Pi^2/6 - Dilog(1-x) L2(2) = Pi^2/4 + Log(2) */ return (log (x) * (1 - log (x-1)) + Pi ^ 2 / 6 - real (dilog (1 - x))) } /* L3(x) = { int L2(x-1)/x dx = int (1 - Log[x-1] + Log[x-1]*Log[x-2] + PolyLog[2,2-x] + Pi^2/12) / x = Log[x] + Log(x) * (Log(1-x) - Log(x-1)) + Dilog(x) + (huge term, fearsome) - PolyLog[3,2-x] + Pi^2 / 12 * Log[x] } */ rhoexact(x) = { if (x <= 0, return (0)); if (x <= 1, return (1)); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{x} 1/t dt = 1 - (log(x) - log(1)) = 1 - log(x) */ if (x <= 2, return (1 - log(x))); /* 1 - int_{1}^{x} rho(t-1)/t dt = 1 - int_{1}^{2} 1/t dt - int_{2}^{x} (1-log(t-1))/t dt = 1 - log(2) - (L2(x) - L2(x)) simplified, see L2() function. The real() is there because Pari returns a complex result for dilog(x), x<~-0.7, with very small imaginary part, even though the result should be purely real */ if (x <= 3, return (1 - log (x) * (1 - log (x - 1)) + real (dilog (1 - x)) + Pi ^ 2 / 12)); return; } /* With invh = 200, rho(8) = 0.000000032319, Knuth/Pardo say ...21, rho(9) = 0.000000001015, Knuth/Pardo say ...16 With invh = 400, all digits match Knuth/Pardo (after rounding) */ tablemax = 10; invh = 256; h = 1. / invh; rhotable = listcreate (tablemax * invh); for (i = 1, 3 * invh, listput (rhotable, rhoexact (i * h), i)) /* Boole's rule. The h conveniently cancel */ for (i = 3 * invh + 1, tablemax * invh, listput (rhotable, rhotable[i - 4] - 2. / 45. * ( 7. * rhotable[i - invh - 4] / (i - 4.) + 32. * rhotable[i - invh - 3] / (i - 3.) + 12. * rhotable[i - invh - 2] / (i - 2.) + 32. * rhotable[i - invh - 1] / (i - 1.) + 7. * rhotable[i - invh] / i ), i ) ) /* The rho function as defined by Karl Dickman, or by Knuth/Trapp Pardo (4.1)-(4.4) */ dickmanrho (alpha) = { local (a, rho1, rho2); if (alpha <= 0., return (0.)); if (alpha <= 3., return (rhoexact (alpha))); if (alpha < tablemax, a = floor (alpha * invh); rho1 = rhotable[a]; rho2 = rhotable[a + 1]; /* Linear interpolation. Should use a better model */ return (rho1 + (rho2 - rho1) * (alpha / h - a)); ); return (0.); } /* The number if x^(1/alpha)-smooth integers below x with first correction term, (4.8), (4.15) */ dickmanrhosigma (alpha, x) = { local (ai, rhoa, rhoa1); if (alpha <= 0., return (0.)); if (alpha <= 1., return (1.)); if (alpha < tablemax, return (dickmanrho (alpha) + (1. - Euler) * dickmanrho (alpha - 1.) / log (x)); ); return (0.); } /* Same, but ai is an index to rhotable, i.e. ai*h = alpha */ dickmanrhosigma_i (ai,x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= tablemax * invh, return (rhotable[ai] + (1. - Euler) * rhotable[ai-invh] / log (x)) ); return (0.); } /* The density of x^(1/alpha)-smooth integers around x */ dickmanlocal (alpha, x) = { if (alpha <= 0, return (0.)); if (alpha <= 1, return (1.)); /* Avoid case where alpha >= tablemax, but alpha - 1 < tablemax which would give negative result */ if (alpha < tablemax, return (dickmanrhosigma (alpha, x) - dickmanrhosigma (alpha - 1, x) / log (x)) ); return (0); } dickmanlocal_i (ai, x) = { if (ai <= 0, return (0.)); if (ai <= invh, return (1.)); if (ai <= 2 * invh, /* dickmanrhosigma_i(ai, x) - dickmanrhosigma_i(ai-invh, x)/log(x), simplified */ return (rhotable[ai] - Euler * rhotable[ai - invh] / log(x)) ); if (ai <= tablemax * invh, return ( rhotable[ai] - (Euler * rhotable[ai - invh] + (1. - Euler) * rhotable[ai - 2 * invh] / log (x)) / log (x) ) ); return (0); } /* Probability that a number around x has all prime factors <=x^alpha, and exactly one >x^alpha, <=x^(alpha*beta) */ dickmanmu (alpha, beta, x) = { local (a, ai, b, bi); ai = ceil ((alpha - beta) * invh); a = ai * h; bi = floor ((alpha - 1) * invh); b = bi * h; return ( h * ( /* Trapezoidal rule. Could be improved */ sum (i = ai, bi, dickmanlocal_i (i, x) / (alpha - i * h)) - (dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ) + (a - alpha + beta) * ( dickmanlocal_i (ai, x) / (alpha - a) + dickmanlocal (alpha - beta, x) / beta ) / 2. + (alpha - 1. - b) * (dickmanlocal (alpha - 1., x) + dickmanlocal_i (bi, x) / (alpha - b)) / 2. ); } brentsuyama (B1, B2, N, nr) = { local (a, ai, i, alpha, beta); alpha = log (N) / log (B1); beta = log (B2) / log (B1); ai = floor ((alpha - beta) * invh); a = ai * h; return ( h * ( sum (i = 1, ai - 1, dickmanlocal_i (i, N) / (alpha - i * h) * (1 - exp(-nr * B1 ^ (-alpha + i * h))) ) /* Between 0 and h, rho() is 1 everywhere except at 0, so we take it as 1 */ + (1 - exp(-nr / B1 ^ alpha)) / 2. + dickmanlocal_i (ai, N) / (alpha - a) * (1 - exp(-nr * B1 ^ (-alpha + a))) / 2. ) + (alpha - beta - a) * ( dickmanlocal_i (ai, N) / (alpha - a) + dickmanlocal (alpha - beta, N) / beta ) / 2. ); } /* Probability that the difference of two S-th Dickson polynomials, each at nr random but distinct points, includes a prime p > B2 so that N / p is B1-smooth. The linear factors of Dickson_S(a)-Dickson_S(b) are assumed < B2 ! */ brsudickson (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S) / 2; for (i = 1, S / 2, if (gcd (i, S) == 1, /* redundancy could be avoided by counting how often each gcd(i,S) value occurs */ n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) + gcd (i + 1, S) - 4) / 2) ) ); return (n / phi); } /* Same, but for S-th power */ brsupower (B1, B2, N, nr, S) = { local (i, n, phi); n = 0; phi = eulerphi (S); for (i = 1, S, if (gcd (i, S) == 1, n = n + brentsuyama (B1, B2, N, nr * (gcd (i - 1, S) - 2)) ) ); return (n / phi); } /* The probability of ECM finding a factor near N with stage 1 parameter B1, stage 2 parameter B2, and nr random but distinct points in stage 2 with the (-S)-th Dickson polynomial (if S < 0) or the S-th power (S > 0) as the Brent-Suyama function */ ecmprob (B1, B2, N, nr, S) = { local (alpha, beta, stage1, stage2, brsu); alpha = log (N/12.) / log (B1); beta = log (B2) / log (B1); stage1 = dickmanlocal (alpha, N / 12.); stage2 = 0; if (B2 > B1, stage2 = dickmanmu (alpha, beta, N / 12.)); brsu = 0; if (S < -1, brsu = brsudickson (B1, B2, N / 12., nr, -S * 2) ); if (S > 1, brsu = brsupower (B1, B2, N / 12., nr, S * 2) ); /* print ("dickmanecm: stage 1: ", stage1, ", stage 2: ", stage2, ", Brent-Suyama: ", brsu); */ return (stage1 + stage2 + brsu) } 1./ecmprob(1000000,100000000,sqrt(10)*10^34,5*4320^2,-6) Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1200.8796622338720043522991602435422102 ? Errors (if any) and Timing Info: Timing: real 0m0.222s user 0m0.217s sys 0m0.005s '68.85.1' ************** PARI ***************** Host 68.85.131.94 (68.85.131.94) Time: Wed Sep 29 17:06:45 2004 Input: yhjhjhj Output: ? yhjhjhj ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.004s '68.85.1' ************** PARI ***************** Host 68.85.131.94 (68.85.131.94) Time: Wed Sep 29 17:07:21 2004 Input: calc Output: ? calc ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '24.35.8' ************** PARI ***************** Host 24.35.89.83 (24.35.89.83) Time: Thu Sep 30 00:20:25 2004 Input: 596501*9634321 Output: ? 5746882110821 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '212.19.' ************** PARI ***************** Host 212.19.143.148 (212.19.143.148) Time: Thu Sep 30 02:31:46 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 06:04:31 2004 Input: x=4 x^2= Output: ? 4 ? ? Errors (if any) and Timing Info: *** unexpected character: x^2= ^-- Timing: real 0m0.009s user 0m0.002s sys 0m0.009s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 06:05:10 2004 Input: x=4 Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 06:05:38 2004 Input: gp Output: ? gp ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:56:57 2004 Input: gcd(6,4) Output: ? 2 ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.003s sys 0m0.009s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:57:23 2004 Input: gcd(173,168) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:58:12 2004 Input: 173 is prime Output: ? 173 ? Errors (if any) and Timing Info: *** Warning: unused characters: isprime. Timing: real 0m0.021s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:58:34 2004 Input: ? isprime 173 Output: ? ? Errors (if any) and Timing Info: *** isprime173: unknown identifier. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 09:59:27 2004 Input: ?isprime Output: ? isprime(x,{flag=0}): if flag is omitted or 0, true(1) if x is a (proven) prime number, false(0) if not. If flag is 1, the primality is certified by the Pocklington-Lehmer Test. If flag is 2, the primality is certified using the APRCL test. ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:00:13 2004 Input: 173 isprime Output: ? 173 ? Errors (if any) and Timing Info: *** Warning: unused characters: isprime. Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:00:51 2004 Input: ?173 Output: ? ? Errors (if any) and Timing Info: *** no such section in help: ?: 173 ^--- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:01:56 2004 Input: isprime(173) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:10:51 2004 Input: ?addprimes Output: ? addprimes({x=[]}): add primes in the vector x (with at most 100 components) to the prime table. x may also be a single integer. The "primes" may in fact be composite, obtained for example by the function factor(x,0), and in that case the message "impossible inverse modulo" will give you some factors. List the current extra primes if x is omitted. If some primes are added which divide non trivially the existing table, suitable updating is done. ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.005s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:11:57 2004 Input: addprime({x=[]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprime({x=[]}) ^-------- Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:12:12 2004 Input: addprime({x=[1]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprime({x=[1]}) ^--------- Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:12:28 2004 Input: ?addprime Output: ? ? Errors (if any) and Timing Info: *** addprime: unknown identifier. Timing: real 0m0.009s user 0m0.006s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:12:57 2004 Input: addprimes({v=[]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({v=[]}) ^-------- Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:10 2004 Input: ?addprimes Output: ? addprimes({x=[]}): add primes in the vector x (with at most 100 components) to the prime table. x may also be a single integer. The "primes" may in fact be composite, obtained for example by the function factor(x,0), and in that case the message "impossible inverse modulo" will give you some factors. List the current extra primes if x is omitted. If some primes are added which divide non trivially the existing table, suitable updating is done. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:41 2004 Input: addprimes({x=[]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({x=[]}) ^-------- Timing: real 0m0.009s user 0m0.001s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:49 2004 Input: addprimes({x=[1]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({x=[1]}) ^--------- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:13:52 2004 Input: addprimes({x=[1]}) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: addprimes({x=[1]}) ^--------- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:14:53 2004 Input: ?prime Output: ? prime(n): returns the n-th prime (n C-integer) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.001s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:15 2004 Input: prime(31) Output: ? 127 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:24 2004 Input: prime(35) Output: ? 149 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:33 2004 Input: prime(42) Output: ? 181 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:38 2004 Input: prime(41) Output: ? 179 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:15:44 2004 Input: prime(40) Output: ? 173 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:16:31 2004 Input: ?divisors Output: ? divisors(x): gives a vector formed by the divisors of x in increasing order. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:16:48 2004 Input: divisors(143) Output: ? [1, 11, 13, 143] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:17:15 2004 Input: ?eulerphi Output: ? eulerphi(x): Euler's totient function of x. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:17:34 2004 Input: eulerphi(17) Output: ? 16 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:17:45 2004 Input: eulerphi(12) Output: ? 4 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:18:16 2004 Input: ?factor Output: ? factor(x,{lim}): factorization of x. lim is optional and can be set whenever x is of (possibly recursive) rational type. If lim is set return partial factorization, using primes up to lim (up to primelimit if lim=0) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.002s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:18:55 2004 Input: factor(143) Output: ? [11 1] [13 1] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.002s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:19:31 2004 Input: ?factormod Output: ? factormod(x,p,{flag=0}): factorization mod p of the polynomial x using Berlekamp. flag is optional, and can be 0: default or 1: simple factormod, same except that only the degrees of the irreducible factors are given. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:20:24 2004 Input: ?primes Output: ? primes(n): returns the vector of the first n primes (n C-integer) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:21:49 2004 Input: 2^3+123 Output: ? 131 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:24:26 2004 Input: ?card Output: ? ? Errors (if any) and Timing Info: *** card: unknown identifier. Timing: real 0m0.009s user 0m0.008s sys 0m0.001s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:25:24 2004 Input: ?Mod Output: ? Mod(x,y,{flag=0}): creates the object x modulo y. flag is optional, and can be 0: default, creates on the Pari stack, or 1: creates a permanent object on the heap. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:06 2004 Input: ?4 Output: ? addprimes bestappr bezout bezoutres bigomega binomial chinese content contfrac contfracpnqn core coredisc dirdiv direuler dirmul divisors eulerphi factor factorback factorcantor factorff factorial factorint factormod ffinit fibonacci gcd hilbert isfundamental isprime ispseudoprime issquare issquarefree kronecker lcm moebius nextprime numbpart numdiv omega precprime prime primes qfbclassno qfbcompraw qfbhclassno qfbnucomp qfbnupow qfbpowraw qfbprimeform qfbred qfbsolve quadclassunit quaddisc quadgen quadhilbert quadpoly quadray quadregulator quadunit removeprimes sigma sqrtint znlog znorder znprimroot znstar ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:18 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:41 2004 Input: ?5 Output: ? elladd ellak ellan ellap ellbil ellchangecurve ellchangepoint elleisnum elleta ellglobalred ellheight ellheightmatrix ellinit ellisoncurve ellj elllocalred elllseries ellminimalmodel ellorder ellordinate ellpointtoz ellpow ellrootno ellsigma ellsub elltaniyama elltors ellwp ellzeta ellztopoint ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:49 2004 Input: ?1 Output: ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:26:58 2004 Input: ?2 Output: ? List Mat Mod Pol Polrev Qfb Ser Set Str Strchr Strexpand Strtex Vec Vecsmall binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:27:21 2004 Input: ?Pol Output: ? Pol(x,{v=x}): convert x (usually a vector or a power series) into a polynomial with variable v, starting with the leading coefficient. ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.002s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 10:39:38 2004 Input: 2^4*3^3 Output: ? 432 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '83.29.2' ************** PARI ***************** Host 83.29.28.90 (83.29.28.90) Time: Thu Sep 30 10:43:47 2004 Input: 3(3^2+1)/2 Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: (3^2+1)/2. Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '83.29.2' ************** PARI ***************** Host 83.29.28.90 (83.29.28.90) Time: Thu Sep 30 10:44:56 2004 Input: 3(3^2+1)/2=15 Output: ? 3 ? Errors (if any) and Timing Info: *** Warning: unused characters: (3^2+1)/2=15. Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '83.29.2' ************** PARI ***************** Host 83.29.28.90 (83.29.28.90) Time: Thu Sep 30 10:45:18 2004 Input: 15=45 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: 15=45 ^---- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:01:40 2004 Input: ?1 Output: ? divrem lex max min shift shiftmul sign vecmax vecmin ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:01:49 2004 Input: ?0 Output: ? x ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:02:00 2004 Input: ?2 Output: ? List Mat Mod Pol Polrev Qfb Ser Set Str Strchr Strexpand Strtex Vec Vecsmall binary bitand bitneg bitnegimply bitor bittest bitxor ceil centerlift changevar component conj conjvec denominator floor frac imag length lift norm norml2 numerator numtoperm padicprec permtonum precision random real round simplify sizebyte sizedigit truncate valuation variable ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:02:30 2004 Input: ?3 Output: ? Euler I Pi abs acos acosh agm arg asin asinh atan atanh bernfrac bernreal bernvec besselh1 besselh2 besseli besselj besseljh besselk besseln cos cosh cotan dilog eint1 erfc eta exp gamma gammah hyperu incgam incgamc lngamma log polylog psi sin sinh sqr sqrt sqrtn tan tanh teichmuller theta thetanullk weber zeta ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:03:17 2004 Input: sqrt(2491) Output: ? 49.909918853871121075615758305504873551 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.007s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:04:19 2004 Input: x=2491 49^2-x Output: ? 2491 ? -90 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '147.162' ************** PARI ***************** Host 147.162.114.40 (147.162.114.40) Time: Thu Sep 30 11:04:51 2004 Input: x=2491 50^2-x Output: ? 2491 ? 9 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '213.35.' ************** PARI ***************** Host 213.35.248.103 (213.35.248.103) Time: Thu Sep 30 16:07:01 2004 Input: f(x) = x+2 f(25) Output: ? ? 27 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '213.35.' ************** PARI ***************** Host 213.35.248.103 (213.35.248.103) Time: Thu Sep 30 16:07:13 2004 Input: f(x) = x+2 f(25) Output: ? ? 27 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '213.35.' ************** PARI ***************** Host 213.35.248.103 (213.35.248.103) Time: Thu Sep 30 16:07:18 2004 Input: f(x) = x+2; f(25) Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.005s '148.205' ************** PARI ***************** Host 148.205.196.207 (148.205.196.207) Time: Thu Sep 30 17:23:59 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '148.205' ************** PARI ***************** Host 148.205.196.207 (148.205.196.207) Time: Thu Sep 30 17:24:34 2004 Input: ifactor(42344); Output: ? ? Errors (if any) and Timing Info: *** unknown function or error in formal parameters: ifactor(42344); ^--------------- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '148.205' ************** PARI ***************** Host 148.205.196.207 (148.205.196.207) Time: Thu Sep 30 17:24:50 2004 Input: factor(42344); Output: ? ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '141.99.' ************** PARI ***************** Host 141.99.112.99 (141.99.112.99) Time: Fri Oct 1 09:02:22 2004 Input: primes(2^300) Output: ? ? Errors (if any) and Timing Info: *** impossible assignment I-->S Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '141.99.' ************** PARI ***************** Host 141.99.112.99 (141.99.112.99) Time: Fri Oct 1 09:03:21 2004 Input: primes(2^15) Output: ? [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, 4079, 4091, 4093, 40[+++] ? Errors (if any) and Timing Info: Timing: real 0m0.020s user 0m0.010s sys 0m0.010s '130.235' ************** PARI ***************** Host 130.235.5.15 (130.235.5.15) Time: Fri Oct 1 18:43:53 2004 Input: F2 := FiniteField(2); Rb := PolynomialRing(F2); Pb := z^8+z^7+z^5+z^3+1; Fb := ext< F2 | Pb >; Ra := PolynomialRing(Fb); Pa :=y^4 + b^23*y^2 + b^48*y + b^239; Fa := ext< Fb | Pa>; Output: ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Errors (if any) and Timing Info: *** unexpected character: F2:=FiniteField(2); ^----------------- *** unexpected character: Rb:=PolynomialRing(F2 ^-------------------- *** unexpected character: Pb:=z^8+z^7+z^5+z^3+1; ^-------------------- *** unexpected character: Fb:=ext; ^-------------- *** unexpected character: Ra:=PolynomialRing(Fb ^-------------------- *** unexpected character: Pa:=y^4+b^23*y^2+b^48* ^-------------------- *** unexpected character: Fa:=ext; ^-------------- Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Oct 1 21:16:21 2004 Input: polroots(t^7-10*t^5+15*t+5,t) Output: ? ? Errors (if any) and Timing Info: *** this should be an integer: ...lroots(t^7-10*t^5+15*t+5,t) ^-- Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Oct 1 21:16:35 2004 Input: polroots(t^7-10*t^5+15*t+5) Output: ? [-3.1404055499933226795309181312088379193 + 0.E-38*I, -1.0326291777230510661764404208905927807 + 0.E-38*I, -0.33616291367665955187567025555163601513 + 0.E-38*I, 1.2240391489606568351016059767239666043 + 0.E-38*I, 3.1349957859561454402143908930036408448 + 0.E-38*I, 0.075081353238115511133515968961729633009 - 1.0906925270223230614181269769106148080*I, 0.075081353238115511133515968961729633009 + 1.0906925270223230614181269769106148080*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.031s user 0m0.009s sys 0m0.009s '130.123' ************** PARI ***************** Host 130.123.128.114 (130.123.128.114) Time: Fri Oct 1 21:18:03 2004 Input: polroots(7*t^6-50*t^4+15) Output: ? [-2.6646487187671384468288849167903923728 + 0.E-38*I, -0.75566037524740221237709057333202109750 + 0.E-38*I, 0.75566037524740221237709057333202109750 + 0.E-38*I, 2.6646487187671384468288849167903923728 + 0.E-38*I, 0.E-38 + 0.72699260951487969538996615411691019901*I, 0.E-38 - 0.72699260951487969538996615411691019901*I]~ ? Errors (if any) and Timing Info: Timing: real 0m0.011s user 0m0.005s sys 0m0.007s '217.128' ************** PARI ***************** Host 217.128.165.34 (217.128.165.34) Time: Sat Oct 2 15:11:29 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '217.128' ************** PARI ***************** Host 217.128.165.34 (217.128.165.34) Time: Sat Oct 2 15:11:59 2004 Input: mathilbert(4) Output: ? [1 1/2 1/3 1/4] [1/2 1/3 1/4 1/5] [1/3 1/4 1/5 1/6] [1/4 1/5 1/6 1/7] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '24.163.' ************** PARI ***************** Host 24.163.67.137 (24.163.67.137) Time: Sat Oct 2 20:38:44 2004 Input: isprime(93765148492242264567029972255389350259464798239451657084614346917544207303437017955778498518892186487775118891243248166551193560238678154222030471135346171589706161232448266715976868851392806655819280199034662286366335385787715566578868562458753495442936870044120123060287256617835002677172150130389096817830440707819595743475905812319746873814938471290537042994565688636675227598251281361269910873320686397937702756298056910147418903972497581686633504786552830388193255547719196203688678295088373840072848219875279138255237582427777746396717849638757745880930385332714682685210249834687435279645620019567449545258236711196234206995621852473973037600952366485124085377638006543147877639254951338300587939502432425544557152465872240259812120295419623677181821041108312706298086584081806164223357592908717748875674823222242283587529410026360045380548699090922495157883134815716379269137533273835179641823093105863823759516081813095147630344718580367225923653064123453445882459206401831073108402162148861789366899914173308862186733844461466576176748932119573982709258772054289548086065532491022520617817438570083902593621001522373) Output: ** WARNING: Computation used more memory than allowed. ** ? ? Errors (if any) and Timing Info: *** the PARI stack overflows ! current stack size: 8000000 (7.629 Mbytes) [hint] you can increase GP stack with allocatemem() Timing: real 0m3.802s user 0m3.400s sys 0m0.015s '24.163.' ************** PARI ***************** Host 24.163.67.137 (24.163.67.137) Time: Sat Oct 2 20:39:30 2004 Input: isprime(10882457724216911840228791111154926772453526692453533870975446245163515796795194175191855421148397726142656128323901533563140522112118769137427951738880932930340528218075961574811420850470784095714535204248610413359024722989094205169388503860139) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m13.822s user 0m12.540s sys 0m0.047s '63.241.' ************** PARI ***************** Host 63.241.65.90 (63.241.65.90) Time: Sun Oct 3 00:53:20 2004 Input: F(x)=2*x^2 F(10) Output: ? ? 200 ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '80.170.' ************** PARI ***************** Host 80.170.31.206 (80.170.31.206) Time: Sun Oct 3 03:03:16 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m0.084s user 0m0.004s sys 0m0.009s '66.169.' ************** PARI ***************** Host 66.169.137.157 (66.169.137.157) Time: Sun Oct 3 15:13:28 2004 Input: mathilbert(3) Output: ? [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Errors (if any) and Timing Info: Timing: real 0m0.016s user 0m0.005s sys 0m0.005s '66.169.' ************** PARI ***************** Host 66.169.137.157 (66.169.137.157) Time: Sun Oct 3 15:13:58 2004 Input: o3 mathilbert(3) Output: ? o3 ? [1 1/2 1/3] [1/2 1/3 1/4] [1/3 1/4 1/5] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:31:38 2004 Input: a+Sqrt(a^2+b); Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: a+Sqrt(a^2+b); ^------ Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:31:49 2004 Input: a+Sqrt(a^2+b) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: a+Sqrt(a^2+b) ^----- Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:32:03 2004 Input: a+sqrt(a^2+b) Output: ? ? Errors (if any) and Timing Info: *** 2 should divide valuation (= 1) in sqrtn. Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:32:17 2004 Input: a+sqrt(a^2+b)=0 Output: ? ? Errors (if any) and Timing Info: *** unexpected character: a+sqrt(a^2+b)=0 ^--- Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '83.129.' ************** PARI ***************** Host 83.129.243.192 (83.129.243.192) Time: Sun Oct 3 15:32:46 2004 Input: sqrt(a^2+b)=-a Output: ? ? Errors (if any) and Timing Info: *** unexpected character: sqrt(a^2+b)=-a ^---- Timing: real 0m0.009s user 0m0.004s sys 0m0.007s '134.82.' ************** PARI ***************** Host 134.82.104.102 (134.82.104.102) Time: Sun Oct 3 22:12:52 2004 Input: "Replace this by some code, then click [PARI] or [MAGMA]!" Output: ? "Replace this by some code, then click [PARI] or [MAGMA]!" ? Errors (if any) and Timing Info: Timing: real 0m3.394s user 0m0.005s sys 0m0.009s '80.58.3' ************** PARI ***************** Host 80.58.3.235 (80.58.3.235) Time: Mon Oct 4 18:46:43 2004 Input: 123456789^12345 Output: ? 5654486280073803310290180594951405950850756477699818775556017861442082882683751453688537977423471844951416047026558934644990166000933155967967928464383198582942849347537979532022676988293878450451007849562469818382431052947092429668386990500711362538468456239004924300455953003962732800885306294109406111828615683010389028238065540377192905035352592097228157740682318633268815966716635430982674394658388984952419989176798733112564021428729778158755197379363828379245013509331118049131705623492027163432765353181559439096591214528906958479766117332571355174718480826163425102431231697153436335264147999803123080957216238309318741217052093409303597960086034966266525676184806636605409620712815872277046006828633135559276122977252403982859529084791171743709142328193989158472680885085951996868638160443922137747867323379350407430890287782144424668143820094093292303548349588889191204701652555050550560290425143017440605178441266483835184244033215736485915452568183081870901013326627529887994705995397915642236980304081882699455851996656414791589060902341162158827324107038566151513832337131425506384835540832367609743309854345740423091391083628849307320834996477477356312574126057771379655426227166099856703411175555112233204520210449082785877874593757246898664441228840871574828048744634364340624989183616163331436964493208107211498120938457489905736960342523511703849014308984674531161318041241246185798473649498398788418772691183709970885464354357394830159050899042537716276194614421029962425223675953796209430822320899112944474407071682144552260371754257973975287684547244805798523764951758073274849789484766080458753980937860446041062791025490167244514642985907398660443252060314671342702009122115686657125470896649899598484981619384744758872993600089106664996402104076036333675514467257900903939778895626327629577557637573104099973443144869296945181301613150129222652299698535448901785770543734041895255171145565162939494718284905449813770305549705046801659167339538006775761169644687713088959393718146620649994000674336267192280538844561432274884113662663764295066151261299014680308346483514183878891652916991741550037642463088071342360113024436703468370546931985476894629335042697204141858803859152708124294850696944410046663367143977448080678318297418759879509157339811544295840249743853717830349232395757414462211215404283186607622239530796200642308349016836089709365038767630367259618504023972269531878319565085010582876030546559335969309103702359363833203566500324424125884952024962619954011456356464510021053351320123377815436356639164125060287998752461135377064387644586966747003157400412741632695309173801802579270412224907314768672413671497225659525033539286868380525931023816512284007663134113007747945143200159687534687468350306066660223573897797343376593678966005523630129301783809147907664972271994996159631147389051675544340814016302491680233675765193835240309828429528175842618338844567293966191560796007803341521061801199812139192156892504905510192802482443116649573541974231084022373585668123475663905193891869032298475305973430582872042381032800888409036436687641942277578793791202824497190838609184471388046861361915986507130377685476310365017104551897843943575306252[+++] ? Errors (if any) and Timing Info: Timing: real 0m5.070s user 0m2.084s sys 0m0.032s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:27:43 2004 Input: 23^2 Output: ? 529 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:28:08 2004 Input: isprime(23^2) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:28:20 2004 Input: isprime(17) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:29:21 2004 Input: isprime(149) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:30:37 2004 Input: isprime(7837) Output: ? 0 ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 00:31:24 2004 Input: isprime(25261) Output: ? 1 ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.005s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:52:12 2004 Input: binomial(1,k) Output: ? ? Errors (if any) and Timing Info: *** this should be an integer: binomial(1,k) ^-- Timing: real 0m0.180s user 0m0.004s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:54:40 2004 Input: vector(10,k,binomial(1,k)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.030s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:54:51 2004 Input: vector(10,k,binomial(2,k)) Output: ? [2, 1, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:55:26 2004 Input: vector(10,k,binomial(3,k)) Output: ? [3, 3, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:55:39 2004 Input: vector(10,k,binomial(4,k)) Output: ? [4, 6, 4, 1, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.026s user 0m0.006s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:55:54 2004 Input: vector(10,k=1,binomial(4,k)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: vector(10,k=1,binomial(4,k)) ^----------------- Timing: real 0m0.010s user 0m0.002s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:05 2004 Input: vector(10,k,binomial(4,k)) Output: ? [4, 6, 4, 1, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:16 2004 Input: vector(10,k,binomial(5,k)) Output: ? [5, 10, 10, 5, 1, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:25 2004 Input: vector(10,k,binomial(6,k)) Output: ? [6, 15, 20, 15, 6, 1, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:36 2004 Input: vector(10,k,binomial(7,k)) Output: ? [7, 21, 35, 35, 21, 7, 1, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.017s user 0m0.003s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:44 2004 Input: vector(10,k,binomial(6,k)) Output: ? [6, 15, 20, 15, 6, 1, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:51 2004 Input: vector(10,k,binomial(7,k)) Output: ? [7, 21, 35, 35, 21, 7, 1, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:56:58 2004 Input: vector(10,k,binomial(8,k)) Output: ? [8, 28, 56, 70, 56, 28, 8, 1, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:57:08 2004 Input: vector(10,k,binomial(9,k)) Output: ? [9, 36, 84, 126, 126, 84, 36, 9, 1, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:57:16 2004 Input: vector(10,k,binomial(10,k)) Output: ? [10, 45, 120, 210, 252, 210, 120, 45, 10, 1] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:57:34 2004 Input: vector(20,k,binomial(11,k)) Output: ? [11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:58:22 2004 Input: vector(20,k,binomial(13,k)) Output: ? [13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:58:36 2004 Input: vector(20,k,binomial(13,k)) Output: ? [13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:59:00 2004 Input: vector(20,k,binomial(11,k)) Output: ? [11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 08:59:18 2004 Input: vector(20,k,binomial(1,k)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:04:27 2004 Input: vector(20,k,binomial(2,k)) Output: ? [2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:04:58 2004 Input: vector(20,k,binomial(3,k)) Output: ? [3, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:05:18 2004 Input: vector(20,k,binomial(4,k)) Output: ? [4, 6, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.007s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:05:58 2004 Input: vector(20,k,binomial(5,k)) Output: ? [5, 10, 10, 5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.008s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:06:31 2004 Input: vector(20,k,binomial(7,k)) Output: ? [7, 21, 35, 35, 21, 7, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:07:12 2004 Input: vector(20,k,binomial(9,k)) Output: ? [9, 36, 84, 126, 126, 84, 36, 9, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.003s sys 0m0.007s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:07:32 2004 Input: vector(20,k,binomial(11,k)) Output: ? [11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:10:05 2004 Input: vector(20,k,binomial(13,k)) Output: ? [13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:10:44 2004 Input: vector(20,k,binomial(15,k)) Output: ? [15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:11:26 2004 Input: vector(20,k,binomial(31,k)) Output: ? [31, 465, 4495, 31465, 169911, 736281, 2629575, 7888725, 20160075, 44352165, 84672315, 141120525, 206253075, 265182525, 300540195, 300540195, 265182525, 206253075, 141120525, 84672315] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:11:42 2004 Input: vector(40,k,binomial(31,k)) Output: ? [31, 465, 4495, 31465, 169911, 736281, 2629575, 7888725, 20160075, 44352165, 84672315, 141120525, 206253075, 265182525, 300540195, 300540195, 265182525, 206253075, 141120525, 84672315, 44352165, 20160075, 7888725, 2629575, 736281, 169911, 31465, 4495, 465, 31, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:12:20 2004 Input: vector(40,k,binomial(63,k)) Output: ? [63, 1953, 39711, 595665, 7028847, 67945521, 553270671, 3872894697, 23667689815, 127805525001, 615790256823, 2668424446233, 10468434365991, 37387265592825, 122131734269895, 366395202809685, 1012974972473835, 2588713818544245, 6131164307078475, 13488561475572645, 27619435402363035, 52728013040874885, 93993414551124795, 156655690918541325, 244382877832924467, 357174975294274221, 489462003181042451, 629308289804197437, 759510004936100355, 860778005594247069, 916312070471295267, 916312070471295267, 860778005594247069, 759510004936100355, 629308289804197437, 489462003181042451, 357174975294274221, 244382877832924467, 156655690918541325, 93993414551124795] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:12:31 2004 Input: vector(70,k,binomial(63,k)) Output: ? [63, 1953, 39711, 595665, 7028847, 67945521, 553270671, 3872894697, 23667689815, 127805525001, 615790256823, 2668424446233, 10468434365991, 37387265592825, 122131734269895, 366395202809685, 1012974972473835, 2588713818544245, 6131164307078475, 13488561475572645, 27619435402363035, 52728013040874885, 93993414551124795, 156655690918541325, 244382877832924467, 357174975294274221, 489462003181042451, 629308289804197437, 759510004936100355, 860778005594247069, 916312070471295267, 916312070471295267, 860778005594247069, 759510004936100355, 629308289804197437, 489462003181042451, 357174975294274221, 244382877832924467, 156655690918541325, 93993414551124795, 52728013040874885, 27619435402363035, 13488561475572645, 6131164307078475, 2588713818544245, 1012974972473835, 366395202809685, 122131734269895, 37387265592825, 10468434365991, 2668424446233, 615790256823, 127805525001, 23667689815, 3872894697, 553270671, 67945521, 7028847, 595665, 39711, 1953, 63, 1, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:28:22 2004 Input: vector(10,x,if(Mod(x^2,10^2)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.008s sys 0m0.003s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:28:49 2004 Input: Mod(36,100) Output: ? Mod(36, 100) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:29:00 2004 Input: Mod(36,10) Output: ? Mod(6, 10) ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.005s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:29:18 2004 Input: vector(10,x,if(Mod(x^2,10)==x,x,0)) Output: ? [1, 0, 0, 0, 5, 6, 0, 0, 0, 10] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:31:45 2004 Input: vector(9,x,if(Mod(x^2,10)==x,x,0)) Output: ? [1, 0, 0, 0, 5, 6, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.009s user 0m0.003s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:33:03 2004 Input: vector(99,x,if(Mod(x^2,10^2)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.022s user 0m0.006s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:37:36 2004 Input: vector(999,x,if(Mod(x^2,10^2)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 101, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 125, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 176, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 200, 201, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 225, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 276, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 300, 301, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 325, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 400, 401, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 425, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 476, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 500, 501, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 525, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 576, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 600, 601, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 676, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 700, 701, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 725, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 776, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 800, 801, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 825, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 876, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 900, 901, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 925, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 976, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.015s user 0m0.008s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:38:48 2004 Input: vector(999,x,if(Mod(x^2,10^3)==x,x,0)) Output: ? [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 376, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 625, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ? Errors (if any) and Timing Info: Timing: real 0m0.034s user 0m0.006s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:39:40 2004 Input: vector(9999,x,if(Mod(x^2,10^4)==x,x,0)) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.041s user 0m0.030s sys 0m0.004s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:00 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0),0,0) Output: ? ? Errors (if any) and Timing Info: *** expected character: ')' instead of: ...f(Mod(x^2,10^4)==x,x,0),0,0) ^--- Timing: real 0m0.009s user 0m0.004s sys 0m0.005s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:23 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0),0)) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.035s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:39 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0)-)) Output: ? ? Errors (if any) and Timing Info: *** unexpected character: ...,if(Mod(x^2,10^4)==x,x,0)-)) ^--- Timing: real 0m0.128s user 0m0.005s sys 0m0.011s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:42:48 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^4)==x,x,0))) Output: ? 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Errors (if any) and Timing Info: Timing: real 0m0.039s user 0m0.031s sys 0m0.009s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:43:59 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^5)==x,x,0)0)) Output: ? ? Errors (if any) and Timing Info: *** expected character: ',' instead of: ...,if(Mod(x^2,10^5)==x,x,0)0)) ^--- Timing: real 0m0.010s user 0m0.005s sys 0m0.006s '68.118.' ************** PARI ***************** Host 68.118.194.75 (68.118.194.75) Time: Tue Oct 5 09:44:07 2004 Input: vector(9999,x,if( x>999 ,if(Mod(x^2,10^5)==x,x,0),0)) Output: ? 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