> From: Alexander Kruppa [mailto:[EMAIL PROTECTED]] > Torben Schlüntz wrote: > > ... > > Besides I have the question: "why does the advanced facor > algortithm of > > prime95 somtimes find 2 factors"? This happens eg. at M1289, has > > 108817410937 and 15856636079 as factors? > > I'm not quite sure which advanced factor algorithm you mean. There are > two possibilities: ... > Trial factoring: ... > balance by excluding only those f which have factors smaller > than some > limit, in a process called sieving. The optimal sieving > limit depends > on how fast the sieving can be performed, and how long it > takes to test > one surviving candidate. > > Thus, a composite factor can be found if all it's prime factors are > above the sieving limit. I do not know what the current > sieving limits > in Prime95 are, but they surely are <15856636079 for all trial > factoring depths.
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 _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
