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 P1 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 P1, how does it relate to how far one does trial factoring ?
Quote:
Originally Posted by akruppa
How about making the thresholds depend on p (mod 120)? For example, for candidate factors p==1 (mod 120), we know that 120p1, giving P1 a much higher chance of recovering such factors if missed by trial division. Otoh, with p==119 (mod 120), p1 has no prime factors <5 except a single 2, so these are poor candidates for P1 and could be trial divided higher.
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Alex :akruppa:

Quote:
Originally Posted by axn1
Why not go all the way, and eliminate smooth p1'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 P1 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...
Jacob