How far to do trial factoring

[S485122]

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

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.
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Alex :akruppa:

Originally Posted by axn1

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...

Jacob

[Mr. P-1]

Originally Posted by S485122

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.

Alex's post wasn't very clear, but it only makes sense if it is interpretted as referring to candidate factors, not 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 ?

From what Alex said (and I've spent some time thinking about this too, and reached much the same conclusion) it's impractical or impossible to efficiently exclude potential factors certain to be found by P-1. Alex's idea was to exclude some potential factors which are more likely to be found by P-1.

Similarly one could include more of those potential factors which are less likely to be found by P-1.