Mersenne Digest Wednesday, September 6 2000 Volume 01 : Number 775 ---------------------------------------------------------------------- Date: Sun, 03 Sep 2000 15:11:23 +0200 From: Yann Forget <[EMAIL PROTECTED]> Subject: Mersenne: Re: A new series of Mersenne-like Gaussian primes Hi, > From: [EMAIL PROTECTED] > > In 1969 I investigated the series of complex (Gaussian) integers: > s[n] = (1+i)^n - 1. [skip] > I hereby solicit the aid of those in GIMPS et al. to extend this series of > primes! Do you have a program, preferably in C, which would work on Linux ? Yann _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Mon, 04 Sep 2000 16:34:26 +0200 From: Paul Landon <[EMAIL PROTECTED]> Subject: Re: Mersenne: smallest possible factor There is a simple proof without using quadratic thingies. The prime f divides a^(f-1)-1 /* Fermat's Little Theorem */ It may first divide a Mersenne number with a smaller exponent, call it a^E-1 and then all exponents that are multiples of E, one of which equals f-1, let's call it EK = f-1. (f-1) is even, call it 2kE. So for E to be odd and f | a^E-1 then f=2kE+1. Indeed all the powers of 2 that are factors of f-1 must "drop", so f=(2^m)kE+1 for all odd E and all bases that f doesn't divide. Similarly for Fermat divisors, all the other factors of f-1 must "drop" leaving only powers of 2. In base 2 using quadratic residues (whatever they are :-) gives us the 1 or 7 mod 8 for divisors of 2^p-1. Does anyone have any (more) heuristics for the probabilistic distribution of K or 2^m.k, where E=(f-1)/K ?? My shot in the dark is that it is less likely for an f=1 (mod 8) to "drop" 3 powers of 2 and divide 2^E-1 with an odd exponent, E than it would be for another f=7 (mod 8) to "drop" only one. Pr�st, Paul Landon > From: Alexander Kruppa > Subject: Re: Mersenne: smallest possible factor > > Spike Jones wrote: > > > A few weeks ago, I thought someone posted something like: > > > > 2^n-1 where n is prime cannot have any factor smaller than n. > > > > Did I get that right? Is there a simple proof? spike > > Factors of a mersenne number Mp are always of the form f=2*p*k+1, k may be > as small as 1. > The proof that factors are 2kp+1 is not simple as far as I remember and uses > the theory of quadratic residues (and thus I didn't understand it). See it > on Chris Caldwells (superb) page on Prime numbers, > http://www.utm.edu/research/primes/ . > The proof is at http://www.utm.edu/research/primes/notes/proofs/MerDiv.html > > Ciao, > Alex. > _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Tue, 5 Sep 2000 02:27:05 EDT From: [EMAIL PROTECTED] Subject: Mersenne: Assembly optimization I found this while browsing mindlessly: http://www.agner.org/assem/pentopt.htm Rather interesting, if you ask me. I don't know whether it makes me want to learn assembler or run like hell in the other direction. I seem to gather that black magic is taught on that page, which might be useful in optimizing Prime95. (I'll go back to the safe, safe world of C, where I can just type "gcc -s -O3 - -mcpu=i686 -fomit-frame-pointer -ffast-math -funroll-loops -malign-double - -fstrict-aliasing -o foo.exe foo.c" to make everything all right. :-> ) Stephan "NOP" Lavavej _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Tue, 5 Sep 2000 00:03:53 -0700 From: "John R Pierce" <[EMAIL PROTECTED]> Subject: Re: Mersenne: Assembly optimization > I found this while browsing mindlessly: > http://www.agner.org/assem/pentopt.htm > Rather interesting, if you ask me. I don't know whether it makes me want to > learn assembler or run like hell in the other direction. I seem to gather > that black magic is taught on that page, which might be useful in optimizing > Prime95. prime95 is already HEAVILY optimized even beyond what that page describes. _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ Date: Wed, 06 Sep 2000 22:53:17 -0700 From: "Terry S. Arnold" <[EMAIL PROTECTED]> Subject: Mersenne: P-1 Credit Does anyone have any skinny on when we will start getting credit for 1. doing P-1 testing? 2. finding a factor during P-1 testing? Terry Terry S. Arnold 2975 B Street San Diego, CA 92102 USA [EMAIL PROTECTED] (619) 235-8181 (voice) (619) 235-0016 (fax) _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt ------------------------------ End of Mersenne Digest V1 #775 ******************************
