Mersenne Digest Friday, May 25 2001 Volume 01 : Number 856 ---------------------------------------------------------------------- Date: Mon, 21 May 2001 21:55:21 +0000 (GMT) From: Russel Brooks <[EMAIL PROTECTED]> Subject: Mersenne: Wish: Add Time Stamps to Iteration display lines Prime95 Wishlist: Add a time stamp to each line of Prime95's output. I've recently had a problem where another app was running away and using all the extra cycles and Prime95 didn't appear to getting ANY. Normally if things are busy the iteration time goes up; in my case since Prime wasn't getting any cycles it still showed the last iteration line but there wasn't any indication that that it was many minutes old. If the local 24 hour time stamp was also on every line I would be able to instantly see Prime wasn't running (well). Running Prime95 v20.6.1 under Win2000 on PIII 866Mhz. Cheers... Russ _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 22 May 2001 17:03:50 +0200 From: Alexander Kruppa <[EMAIL PROTECTED]> Subject: Re: Mersenne: ECM Question... Alexander Kruppa wrote: > > gp_p(x) | go_p, and p+1-sqrt(p) <= go_p <= p+1+sqrt(p) . Since go_p(x) Correction: I have taken the limits above from my memory which has once again proved itself untrustworthy. The correct limits are p+1-2*sqrt(p) < go_p <= p+1+2*sqrt(p) , a theorem by Haase, which I found in O. Forster, Algorithmische Zahlentheorie. Ciao, Alex. _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 22 May 2001 19:27:31 +0200 From: Alexander Kruppa <[EMAIL PROTECTED]> Subject: Mersenne: Factoring M727 through M(M727) revisited Hi all, I think I found a (although purely theoretical) way to find a factor of M(p) by factoring M(M(p)). Ok here goes: f is a prime factor of M(M(p)), 2^(M(p)) = 1 (mod f) so the order of 2 in Z/f*Z is !=1, divides M(p) but is not neccessarily equal to M(p). Lets call it c. Since the order of 2 also divides f-1, c|f-1. The problem with trial division of M(M(p)) is that you can't limit the candidate divisors to multiples of the factors of M(p) when you know these factors - so you'd have to resort to testing all primes as candidate divisors (or at least those where divisor-1 has a large prime factor). This is impractical for large c and therefore large f. The interesting case is when c != M(p), f != 1 (mod M(p)) and f = 2*k*c+1 for a small k. Then the P-1 method could recover that factor if the bound is >=k or k is smooth and you do an extra exponentiation by M(p), i.e. f = GCD(3^(M(p)*E)-1,M(M(P))), E product of primes and prime powers <=bound. The trick here is that P-1 finds the factor f if the exponent E is any multiple of f-1. You don't have to know c in order to exponentiate by it - - knowing that c|M(p) suffices. GCD(M(p), f-1) will finally recover the factor of M(p). The only drawback is that M(M(727)), and indeed any M(M(P)) for yet unfactored M(p), is so gargantuan that doing arithmetic modulo it is completely out of the question. But the idea looks interesting on paper. Ciao, Alex. _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Tue, 22 May 2001 18:29:30 -0000 From: "Brian J. Beesley" <[EMAIL PROTECTED]> Subject: Mersenne: (OT) k.2^n-1 prime testing project Hi, I was trawling around some of the pages associated with the Proth project yesterday & found that Michael Hartley has started a project to test primality of numbers of the form k.2^n-1 for k > 300. Very little work has been done on these, therefore there are opportunities to find some primes quickly, since the numbers involved are relatively small - there are a number of ranges still available for n between 16000 and 32000, for which one day on a P100 would probably suffice to finish the whole range, and with about an evens chance of finding at least one prime somewhere in the range. This project may be of interest to some people with relatively slow systems capable of running Proth.exe (i.e. wintel systems). The project home page is at http://cis.sit.edu.my/examples/jsp/psearch/start.jsp Note that (although not stated) cookies must be enabled to use the personal account facilities (reservation of ranges, submission of results etc.) Regards Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Wed, 23 May 2001 18:20:28 US/Eastern From: [EMAIL PROTECTED] Subject: Mersenne: A Basic question I know I've hears the answer before, but, what kinds of factoring work does Primenet credit? I spend hours soing p-1 factoring (hours on a P4-1.4GHz), find nothing, and get no credit. I find a factor, and get .001 years of credit. Also, does trial (i.e. the power of two sequence before a LL test) factoring recieve any credit? Thank you: Bradford J. Brown - --------------------------------------------- This message was sent using GSWeb Mail Services. http://www.gasou.edu/gsumail _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 25 May 2001 12:30:32 +0200 From: "Jeroen" <[EMAIL PROTECTED]> Subject: Mersenne: Bug? Hi I was playing around with the client program. When I go to the advanced menu and choose ecm, there I fill in for exponent 101 and check the factor 2^N-1 box and click ok. After about a minute the program says to me : Stage 1 complete. 25964568 transforms, 1 modular inverse. Time: 59.738 sec. (27838040173 clocks) P101 has a factor: 3 Cofactor is a probable prime! If my calculations are correct 2^101-1 = 2535301200456458802993406410751 To check if this is divisible by 3 add al digits and check if the sum is divisible by 3 Total of digits is 112 so 3 is not a factor. Is this a bug in the client? or do i make an error somewhere? Regards, Jeroen _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ End of Mersenne Digest V1 #856 ******************************
