Hello, everyone! I sent a letter to this list about a month ago indicating that Fermat number factoring by the Elliptic Curve Method could be done more efficiently by running curves on numbers of the form 2^(2^n) - 1 ("M-numbers") instead of running on the Fermat numbers themselves of the form 2^(2^n) + 1 ("P-numbers"). I was finding increases in efficiency of 3% to 15% on Athlon and Pentium III computers, mainly because of a wider choice of FFT sizes available to Prime95 on M-numbers than on P-numbers. George Woltman has pointed out that the increase in efficiency on Pentium IV computers is even more dramatic, largely because the FFT code for M-numbers incorporates use of the Pentium-IV specific SSE2 instructions, whereas the code for P-numbers does not use this feature. As an example, I ran curves to B1=44,000,000 on several exponents on a 1900 MHz Pentium IV and came up with the following timings:
P4096 (Fermat-12) : 3 hours, 39 minutes P8192 (Fermat-13): 6 hours, 58 minutes P16384 (Fermat-14): 16 hours, 51 minutes total time for these three curves: 27 hours, 28 minutes Then I ran a single curve on M32768 = 2^32768 - 1. This number is the product of all the Fermat numbers from F0 to F14, and I included all known factors < 60 digits of these Fermat numbers in the lowm.txt file. (Of course F0 through F11 are already completely factored.) The result: M32768: 10 hours, 16 minutes Quite a dramatic increase in speed! George has now added the factors of these M-numbers to the lowm.txt file, and has included a note about their use on: http://www.mersenne.org/ecmf.htm The combination of a fast Pentium IV with this SSE2 code makes this 1900 MHz Pentium approximately 10 times as fast as the 400 MHz Pentium II's I was using a year-and-a-half ago! Good luck, anyone who wants to try this. Phil Moore _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers