Feature request: p+1 factorization
 

I would like to see [URL=http://www.mersennewiki.org/index.php/P_Plus_1_Factorization_Method]p+1 factorization[/URL] in some future release of Prime95. The programming should not be difficult since it is similar to p-1 in many aspects, and the duplication of the index is already programmed for the Lucas-Lehmer test. The step 1 could be performed about 30% faster than the naive method shown at the page linked by using [URL=ftp://ftp.cwi.nl/pub/pmontgom/Lucas.ps.gz]Montgomery's PRAC[/URL] algorithm

This would require twice the memory of p-1 and it would be slightly slower than p-1, but we can find some factors using p+1 that would be useful for LMH.

Well, it's of course up to George whether he does this, but at least for Mersennes p+1 is very likely not worth the effort because:

1) The special form of factors of M(p) makes p-1 much more likely to succeed for any given smoothness bounds;

2) Statistically speaking, on average half the times you do a "p+1" run you end up doing p-1 anyway (and probably less efficiently than doing a straight p-1 run would have been) - that's one of the intrinsic properties of the p+1 method.

You are right in both points, but even doing it twice with different parameters (so it has a 75% of success if p+1 is smooth) it is still faster than performing an ECM curve with the same bounds. ECM also has the same smoothness problem like p+1 so it cannot be used for LMH.

I think that p+1 can find some new factors (but with a productivity of about half of p-1).