Running this version: GP/PARI CALCULATOR Version 2.4.2 (development CHANGES-1.1844) i686 running linux (ix86 kernel) 32-bit version compiled: Aug 18 2007, gcc-4.1.2 (Ubuntu 4.1.2-0ubuntu4) (readline v5.2 enabled, extended help enabled)
the manual claims that while the out of factor() contains "primes" which are not proved primes, the function isprime() provides a proof of primality. In which case what is going on here: ? default(debug,2) %5 = 2 ? p=nextprime(10^20) %6 = 100000000000000000039 ? isprime(p) *** isprime: Warning: IFAC: untested integer declared prime. 507526619771207 %7 = 1 It seems that part of the "proof" involves a factorization whose results are not proved. Unless I am misunderstanding what the manual claims, this means that it is _not_ doing what is claimed. One solution would be (as I suggested earlier) to have a flag on factor() to require proof, as this could be passed on down through isprime() calls, and then we could trust the results! John -- John Cremona --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---