ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 26 Aug 2016 17:11:28 -0500What are the speediest algorithms for factoring very large integershttps://ask.sagemath.org/question/34586/what-are-the-speediest-algorithms-for-factoring-very-large-integers/ I'm faced with factoring many CONSECUTIVE large integers. What are the speediest algorithms available for factoring ALL the integers between (say) 10^N + 1 and 10^(N+1) + 1, for N = 10, 11, 12, 13, 14, 15, ... ? For each such N, how much time T(N) would be required to factor these integers? Would the same algorithm be used for each N ? Can some
of these factorizations be accomplished on a Mac at home ?Thu, 25 Aug 2016 19:28:27 -0500https://ask.sagemath.org/question/34586/what-are-the-speediest-algorithms-for-factoring-very-large-integers/Comment by B r u n o for <p>I'm faced with factoring many CONSECUTIVE large integers. What are the speediest algorithms available for factoring ALL the integers between (say) 10^N + 1 and 10^(N+1) + 1, for N = 10, 11, 12, 13, 14, 15, ... ? For each such N, how much time T(N) would be required to factor these integers? Would the same algorithm be used for each N ? Can some
of these factorizations be accomplished on a Mac at home ?</p>
https://ask.sagemath.org/question/34586/what-are-the-speediest-algorithms-for-factoring-very-large-integers/?comment=34603#post-id-34603What you want to do seems unreachable for me (though I may be wrong) using Sage. Note that storing the results is already non trivial: for $N = 10$, even if you count only one bit by integer (of course irrealistic!) it would already require 10Gb if I did not make mistakes.Fri, 26 Aug 2016 17:11:28 -0500https://ask.sagemath.org/question/34586/what-are-the-speediest-algorithms-for-factoring-very-large-integers/?comment=34603#post-id-34603