On Sunday 10 November 2002 20:03, [EMAIL PROTECTED] wrote: > "Brian J. Beesley" <[EMAIL PROTECTED]> wrote > - Here's one example: > - > - With sigma=1459848859275459, Prime95 v22.12 finds the factor > - 777288435261989969 of M1123: > - > - in stage 1 with B1 >= 535489 > - in stage 2 with B1 >= 38917 & B2 >= 534241
And here are some more With sigma=7324432520873427, the factor 649412561933038085071 of M1621 is found - in stage 1 with B1 >= 2546119 - in stage 2 with B1 >= 94727, B2 >= 2543311 With sigma=5643809308022499, the factor 838124596866091911697 of M1787 is found - in stage 1 with B1 >= 378041 - in stage 2 with B1 >= 35543, B2 >= 378001 With sigma=6305161669623833, the factor 597702354293770769 of M1867 is found - in stage 1 with B1 >= 258983 - in stage 2 with B1 >= 3061, B2 >= 258301 With sigma=5956836392428930, the factor 8142767081771726171 of P721 is found - in stage 1 with B1 >= 54779 - in stage 2 with B1 >= 33487, B2 >= 54390 > > How does one map sigma to a curve (and initial point)? > What is the range of sigma (it seems to go beyond 2^32)? At worst, RTFS. My reason for finding the critical B values was in the hope that someone with a better understanding of the algorithms and/or an independent ECM factoring program would be able to confirm that these values make sense. > > The ECM tests should include a case where two primes are found at > the same time during step 2, because the largest primes dividing the > two group orders are equal. [That is, the GCD will be composite.] > This test may be hard to construct, however. Actually, it's very easy. The way I constructed the results submitted so far was to remove the known "target" factor from the low[mp].txt file & run a few curves with B1=10^5, B2 automatic to find a sigma that "works". Not neccessarily the sigma that gives the lowest limits. After receiving this message, I removed _all_ the known factors for P721. This was interesting, and indicates a bug, though it appears to be not very important: with same sigma & minimum B1 & B2 noted above, the composite factor 129 (= 3 * 43) was found. I would have expected (at least) 3*43*8142767081771726171 Placing the known factors 3 & 43 back into lowp.txt and repeating the same curve yielded the expected factor 8142767081771726171. > > Either the ECM tests or the p-1 tests should include a case where > the group order (or p-1) is divisible by a power of a moderate prime, > such as 61^3 or 757^2 . There are lots of known examples for P-1. Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
