What are the speediest algorithms for factoring very large integers

asked 2016-08-25 19:28:27 -0500

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 ?

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What 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.

B r u n o gravatar imageB r u n o ( 2016-08-26 17:11:28 -0500 )edit