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Old 2007-07-22, 10:36   #1
S485122's Avatar
Sep 2006
Brussels, Belgium

2·929 Posts
Default How far to do trial factoring

In a discussion on how far trial factoring should go, there has been a suggestion concerning the fact that some numbers are better candidates for P-1 than others. This should be determined at the start of trial factoring in order to chose to how many bits a Mersenne number should be trial factored, at that time only the exponent of the Mersenne number is known. But in that discussion I am not sure whether one speaks about the factors or the exponents. If one can, indeed, not try some potential factors that would be certain to be found by P-1, how does it relate to how far one does trial factoring ?
Originally Posted by akruppa View Post
How about making the thresholds depend on p (mod 120)? For example, for candidate factors p==1 (mod 120), we know that 120|p-1, giving P-1 a much higher chance of recovering such factors if missed by trial division. Otoh, with p==119 (mod 120), p-1 has no prime factors <5 except a single 2, so these are poor candidates for P-1 and could be trial divided higher.
Alex :akruppa:
Originally Posted by axn1 View Post
Why not go all the way, and eliminate smooth p-1's from TF altogether? Using some additional sieving, smooth p's could be quickly identified and eliminated, resulting in 30% fewer candidates to be checked by TF (of course, all of this assumes that P-1 will be run without fail after TF).
Cfr thread New factoring breakeven points coming.

This thread could be in maths, software of factoring instead of primenet...

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