RE: Mersenne: Composite factors.
> I've found a few composite factors whilst running P-1 on > small exponents. Working on M(32340) with P-1 turned out factors with several hundred digits, even when the B1 limit was set very low. This experiment turned up a bug in Prime95 which George has now fixed. The numbers were so large that their decimal representation overflowed an internal buffer. The same bug was triggered by P(32340) but not quite so vigorously. A special case, certainly, but one which occurred in real life and as part of a serious computation to help prove primality. Paul _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
RE: Mersenne: Composite factors.
The record P-1 factor is 56379662829467477289264041716715663 or 129 bits. -Original Message- I don't think P-1 has found a "proper" factor exceeding 110 bits, yet. _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Composite factors.
On Tuesday 24 September 2002 06:05, Daran wrote: > P-1, like any other GCD-based factorisation method, will yield a composite > result in the event that there are two (or more) prime factors within its > search space. It seems unlikely that this would happen in practice because > unless both were > ~ 64 bits, one of them would most likely have been found > earlier during TF. However given that some factors found have been > 130 > bits, TTBOMK only using ECM - and those events are rare enough to be newsworthy. I don't think P-1 has found a "proper" factor exceeding 110 bits, yet. > then the possibility is there. > > I was wondering if returned factors are checked for primality. I've found a few composite factors whilst running P-1 on small exponents. They've all factorised _very_ easily (well within one minute) using "standard tools". Basically I'm interested enough to do this myself whenever what appears to be an abnormally large factor is found, but it wouldn't be hard to automate. Also very large factors are found at a low enough rate that there's simply no need to distribute the checking. Regards Brian Beesley _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Composite factors.
P-1, like any other GCD-based factorisation method, will yield a composite result in the event that there are two (or more) prime factors within its search space. It seems unlikely that this would happen in practice because unless both were > ~ 64 bits, one of them would most likely have been found earlier during TF. However given that some factors found have been > 130 bits, then the possibility is there. I was wondering if returned factors are checked for primality. Regards Daran G. _ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
