I recently kluged together a script to analyse the factors in my results.txt file for smoothness, and discovered the following results, among others.
P-1 found a factor in stage #2, B1=45000, B2=675000. UID: daran/1, M7893989 has a factor: 34859249922062613959 =2*167*9533*1386901*7893989 P-1 found a factor in stage #2, B1=40000, B2=650000. UID: daran/1, M7726057 has a factor: 24561404952170157528115369 =2^3*3*29*113*863*5861*7726057*7991441 Neither of which were k-smooth to B2 A search on "Pollard's Method" came up with this webpage http://www.users.globalnet.co.uk/~aads/Pminus1.html which lists several more from GIMPS, some of which with unfeasibly large B2 values needed to make the factor k-smooth. One possible explanation for this is pure luck. The P-1 method will find all k-smooth prime factors, but there is no guarantee that other factors won't pop out, just no particular reason to expect them to. The chance of this would seem remote. Another explanation is that I vaguely remember someone saying that an optimisation to the implementation of stage 2 had a side effect of possibly introducing new factors, but I don't remember the details. Can anyone shed any light on this? One of the things I would like to do is to be able to determine, for each factor, what the minimum values of B1 and B2 would have to be for it to have been uncovered by a P-1 test, irrespective of what actual bounds were used, or even if it was found using another method. This is easy to do in the case of the k-smooth factors. Is there any way to characterise these additional ones? Regards Daran G. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
