Re: Mersenne: ECM Question...
While we're on the subject, can someone explain how to derive the group order for factors found using ECM? I've been carrying out ECM on an old PC for almost a year now, and I'd like to be able to derive, and factorise, the group orders for the factors that I've found. I've been making an effort to understand the maths, and I'm getting there slowly, but I've found nothing yet that explains how to derive the group orders. If my understanding is correct, you would need to know the equations used by mprime to derive the co-ordinates of the starting point for each curve. Anyway, if someone could explain how to derive the group order, or point me in the right direction, I'd be very grateful. Regards, Steve If the sigma is the same, then a curve with B1=25 will find any factor that a curve with B1=5 finds. When you run 700 random curves at B1=25, you might theoretically miss a factor that someone else finds with B1=5, if he gets a lucky sigma so that the group order is very smooth. But in general, using the same number of curves, the higher bound should find all the factors that the lower bound can find. But dont be tempted into running only a few curves at very high bounds. The strength of ECM is that you can try curves with different group orders until a sufficiently smooth one comes along. So skipping bound levels is usually not a good idea unless you have reason to believe the the number unter attack has only large factors which call for a higher bound. _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: Another ECM question
Is it (at least) theoretically possible that some larger factors are unfindable with ECM due to the limited number of sigma producable by George's random number generator? Nathan _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Re: Mersenne: Spacing between mersenne primes
On 16 May 2001, at 19:52, Ken Kriesel wrote: At 10:56 AM 5/16/2001 -, Brian J. Beesley [EMAIL PROTECTED] wrote: Another point - we're coming up to the second anniversary of the discovery of M38(?) - I think we're overdue to find another one! It would be nice to find another soon. But I don't think we're overdue. I have an old print of the Mersenne Search Status Page - it's dated 11/11/99. The point at which the one LL and status unknown columns are equal is at about 7.75 million. On today's copy of the same page, the crossover is about 11.5 million. So the ratio is about 1.5. Long ago in Internet time I wrote: [... big snip ...] to droop back to a lower discovery rate. On average there are less than 2 mersenne primes per exponent doubling: 36 / [ln(2976221)/ln(2)] = 1.67 mersenne primes per doubling of exponent, or about 37 / [ln(~300)/ln(2)] = 1.72 Mp's per doubling of p giving a ratio of ~2^(1/1.7) = 1.5. BTW I agree absolutely with the analysis in your message. The interval between the discovery of M37 and M38(?) was shorter than the interval which has elapsed since the discovery of M38(?), despite the unusual (and in the long term unsustainable) increase in power in the CPUs installed in new PC systems during this time. Maybe M39(?) is not massively overdue, but I think it is at least about due now. However, random distribution means we could be unlucky not find another prime for two more years, or possibly even longer... A new discovery would give the project a shot in the arm, though! Regards Brian Beesley _ Unsubscribe list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
Mersenne: [OT] (fwd) [PrimeNumbers] Proth 6.6
For those who are interested, Yves Gallot has released Proth 6.6, which has great speed-ups for some architectures. His post to the PrimeNumbers list follows. Regards, Nathan Proth 6.6 is on the Web. This new release detects CPU with L2 cache on die (new PIII and Celeron, P4) and with large L1 cache (Athlon and Duron). On these processors, a different size is used for internal blocks. On a Celeron 800 for the GFN of the form b^65536+1, the version 6.6 is 10% faster than the 6.5 and 20% faster than the 6.4. Now, on this computer the test of a GFN having less than 3,000,000 digits is as fast as the test of a Mersenne number with Prime95... and there are more GF primes not yet discovered in this range than Mersenne primes! Yves Unsubscribe by an email to: [EMAIL PROTECTED] The Prime Pages : http://www.primepages.org Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
