Paul Leyland wrote: > > > From: Alexander Kruppa [mailto:[EMAIL PROTECTED]]
> Another issue which used to generate multiple factors by trial division in prime95 >(I don't know if it still does) is the following. > > All factors of Mersenne numbers fall into a small number of concisely describable >sets. Prime95 used to test all of one kind of factor in a range before going on to >test all those of a different kind in the same numerical range. The program also >wanted to find the smallest prime factor. Consider now what happens if two factors >in a range belong to different sets. You have to process all sets before you know >which is the smallest. Having found any larger ones, it would be stupid not to >report them too. > > Paul This is actually the more likely cause. You mean the 16 residue classes mod 120 that are 1 or 7 mod 8, and coprime to 120. Versions prior to v19 tried one of these classes all the way to the desired factoring depth before going to the next class, versions since v19 do all classes of one factor bit length before going to the next length. In the old way, 108817410937 would be found first since it is 97 (mod 120), while 15856636079 is 119 (mod 120) and (afaik) Prime95 used to test the classes in ascending order. Also, the composite factor 15856636079*108817410937 has 71 bits, trial factoring such a small exponent to 71 bits would take a terribly long time. Alex _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
