Mersenne Digest Monday, June 16 2003 Volume 01 : Number 1075
---------------------------------------------------------------------- Date: Sat, 14 Jun 2003 13:26:31 +0200 From: Guillermo Ballester Valor <[EMAIL PROTECTED]> Subject: Re: Mersenne: M#40 - what went wrong? Hi, On Saturday 14 June 2003 12:13, Steinar H. Gunderson wrote: > The biggest problem with SSE2 is of course that it's only supported on the > Pentium 4 yet -- they are becoming increasingly common, but for instance, > no current AMD chip supports it. > Actually, new AMD64 chips (current Opteron and future Athlon64) supports SSE2, and doubling the 128 mmx registers ( 8 for Pentium4 and 16 for AMD64). George Woltman, with P4 and SSE2, has made impressive improvements in Prime95. I'm just this weeks adding SSE2 code to Glucas to see how it can run on opterons, but I'm still in beta code. Guillermo. - -- Guillermo Ballester Valor registered linux user #117181 [EMAIL PROTECTED] Ogijares, Granada SPAIN _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 15 Jun 2003 19:52:12 -0700 From: Luke Welsh <[EMAIL PROTECTED]> Subject: Re: Mersenne: M#40 - what went wrong? At 03:16 PM 6/13/03 -0400, George Woltman wrote: >So far I've come up with two possibilities. >[....] >2) This case results from the way my C compiler treats floating point NaN. >NaN stands for not a number. If NaN is converted to an integer, the integer >is zero. So if the FFT data is all NaNs, prime95 will report a prime. Prime95 >check for NaNs every iteration, but if every FFT data value becomes NaN >after the inverse FFT of the last LL iteration, then we get a false positive. >Furthermore, corrupting a single value (the initial carry input to rounding >and carry propogation code) could set every FFT data value to NaN. I'm fishing.... What about +/- INF ? What about corruption of any of the pre-computed arrays? Is there a constant "-2" that could be corrupted? - --Luke _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 16 Jun 2003 12:30:25 +0200 (MET DST) From: Wojciech Florek <[EMAIL PROTECTED]> Subject: Mersenne: P-1, N-1 tests Hi! Recently, I've been playing with some number theoretical problems (just for fun). I've met two similar approches mentioned in the subject: a) P-1 method of factorization and b) N-1 primality test. It seems (if I understand well) that a) we assume that a prime factor p of a given (composite) number n is such that p-1 is smooth; then we can try to determine p itself; b) we _know_ factorization of n-1 and there are some primality tests (see, e.g., Chris Caldwell pages) for n My question is: Is there any method/algorithm to determine _factors_ of n if the factorization of n-1 is known? I understand that there is no _exact_ formula for factors, but maybe there are some strong conditions, which restrict factors to a specific form (like k2^r+1 for Fermat numbers) The second question I should send directly to Chris Caldwell. In his Prime Pages the N-1 test of primality needs such a that a^(N-1)=1 mod N and a^(N-1)/q is not 1 mod N (q is a factor of N-1). Methods for determining the number a are not presented. Are there any such methods? Regards Wojciech Florek (WsF) Adam Mickiewicz University, Institute of Physics ul. Umultowska 85, 61-614 Poznan, Poland phone: (++48-61) 8295033 fax: (++48-61) 8295167 email: [EMAIL PROTECTED] _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Mon, 16 Jun 2003 16:16:12 -0400 From: George Woltman <[EMAIL PROTECTED]> Subject: Re: Mersenne: M#40 - what went wrong? At 07:52 PM 6/15/2003 -0700, Luke Welsh wrote: >I'm fishing.... > >What about +/- INF ? Yes, they would be treated just like a NaN. Prime95 checks if the sum of the FFT inputs is NaN, or +/- INF every iteration (generating the common ILLEGAL SUMOUT error). >What about corruption of any of the pre-computed arrays? Yes, if the first weight value was NaN, then that would corrupt the entire FFT data array. Of course, this generates an ILLEGAL SUMOUT on the next iteration, but if this single corruption happened during the last iteration then a false positive would have been generated. Version 23.5 will now detect this. I'm also adding code to 23.5 to check EVERY iteration for an impossible result such as -2, -1, 0, 1, 2. This test will be very, very quick. FYI, six times a result of 0000000000000002 has been reported to the server. So, somehow or another it is possible for a hardware error to zero the FFT data without triggering an ILLEGAL SUMOUT. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ End of Mersenne Digest V1 #1075 *******************************
