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-   -   How far to do trial factoring (https://www.mersenneforum.org/showthread.php?t=8767)

S485122 2007-07-22 10:36

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 ?[QUOTE=akruppa;55962]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:[/QUOTE][QUOTE=axn1;55991]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).[/QUOTE]Cfr thread [thread=4213]New factoring breakeven points coming[/thread].

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

Jacob

Mr. P-1 2007-09-06 00:52

[QUOTE=S485122;110908]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.[/QUOTE]

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

[QUOTE]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 ?[/QUOTE]

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 [i]certain[/i] to be found by P-1. Alex's idea was to exclude some potential factors which are [i]more likely[/i] 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.


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