Quote:
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 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.

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 P1, 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 P1. Alex's idea was to exclude some potential factors which are
more likely to be found by P1.
Similarly one could include more of those potential factors which are less likely to be found by P1.