Delivered-To: luke@ndatech.com X-Sender: rugeley@pop3.demon.co.uk X-Mailer: QUALCOMM Windows Eudora Version 5.1 Date: Sat, 15 Dec 2001 22:44:30 +0000 To: Luke Welsh From: mersenne-digest-invalid-reply-address@base.com (Mersenne Digest) (by way of Gordon Spence ) Subject: Mersenne Digest V1 #912 Mersenne Digest Sunday, December 2 2001 Volume 01 : Number 912 ---------------------------------------------------------------------- Date: Fri, 30 Nov 2001 07:35:24 -0000 From: "Daran" Subject: Re: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne Newsletter, issue #18) - ----- Original Message ----- From: To: Sent: Saturday, November 24, 2001 6:49 PM Subject: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne Newsletter, issue #18) > But ones factoring benefit calculation might ["should" would be in > line with the popular theme of prescribing what's best for other > GIMPS participants :)] include not only the time savings of > eliminating the need for one or two L-L tests, but also the extra > benefit of finding a specific factor. I can see no way of objectively quantifying this benefit. > In the GIMPS Search Status table at www.mersenne.org/status.htm the > march of progress is from "Status Unknown" to "Composite - One LL" to > "Composite - Two LL" to ... "Composite - Factored". More desireable - whether or not recorded on that page - would be "Composite - Least (or greatest) factor known". Most desireable (other than "Prime") would be "Composite - Completely factored'. > This reflects the view (with which I agree) that it is more valuable > to know a specific factor of a Mnumber than to know that a Mnumber is > composite but not to know any specific factor of that Mnumber. > > So a "Factored" status is better for GIMPS than a "Two LL" status, but > calculations of factoring benefit that consider only the savings of > L-L test elimination are neglecting the difference between those two > statuses. If one consciously wants to neglect that difference ... > well, okay ... but I prefer to see that explicitly acknowledged. It seems to be implicitely acknowledged in the way the trial factoring depths are determined. If one places a non-zero value on a known factor, then the utility of extra factoring work on untested, once tested, and verified composites would be increased. It would have to be set very high indeed to make it worth while returning to verified composite Mersennes. > Richard Woods Daran G. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 30 Nov 2001 02:47:15 -0600 From: "Steve Harris" Subject: Mersenne: Re: Factoring benefit/cost ratio Actually, Richard's statement that "a 'Factored' status is better for GIMPS than a 'Two LL' status" is not quite true. It's better for the mathematical community as a whole, but not for GIMPS. GIMPS is looking for primes, not factors, and without skipping over any. This means all candidates must be tested and the non-primes eliminated, and it doesn't matter whether they are eliminated by 'factored' or by 'two matching nonzero LL residues'. It matters to those who are attempting to fully factor Mersenne numbers, but that's a different project altogether, and one that is decades (at least) behind GIMPS. The only reason we do any factoring at all is to reduce the time spent on LL testing. Besides, if you do manage to find a 75-digit factor of a 2-million-digit Mersenne number, that still leaves a 1999925-digit remainder. Really not much help :-) Regards, Steve Harris - -----Original Message----- From: Daran To: mersenne@base.com Date: Friday, November 30, 2001 2:00 AM Subject: Re: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne Newsletter, issue #18) >----- Original Message ----- >From: >To: >Sent: Saturday, November 24, 2001 6:49 PM >Subject: Factoring benefit/cost ratio (was: Mersenne: Fw: The Mersenne >Newsletter, issue #18) > >> But ones factoring benefit calculation might ["should" would be in >> line with the popular theme of prescribing what's best for other >> GIMPS participants :)] include not only the time savings of >> eliminating the need for one or two L-L tests, but also the extra >> benefit of finding a specific factor. > >I can see no way of objectively quantifying this benefit. > >> In the GIMPS Search Status table at www.mersenne.org/status.htm the >> march of progress is from "Status Unknown" to "Composite - One LL" to >> "Composite - Two LL" to ... "Composite - Factored". > >More desireable - whether or not recorded on that page - would be >"Composite - Least (or greatest) factor known". Most desireable (other than >"Prime") would be "Composite - Completely factored'. > >> This reflects the view (with which I agree) that it is more valuable >> to know a specific factor of a Mnumber than to know that a Mnumber is >> composite but not to know any specific factor of that Mnumber. >> >> So a "Factored" status is better for GIMPS than a "Two LL" status, but >> calculations of factoring benefit that consider only the savings of >> L-L test elimination are neglecting the difference between those two >> statuses. If one consciously wants to neglect that difference ... >> well, okay ... but I prefer to see that explicitly acknowledged. > >It seems to be implicitely acknowledged in the way the trial factoring >depths are determined. If one places a non-zero value on a known factor, >then the utility of extra factoring work on untested, once tested, and >verified composites would be increased. It would have to be set very high >indeed to make it worth while returning to verified composite Mersennes. > >> Richard Woods > >Daran G. > > >_________________________________________________________________________ >Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm >Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 30 Nov 2001 14:31:05 EST From: EWMAYER@aol.com Subject: Mersenne: Re: need access to an SGI Thomas Ritschel has been kind enough to build binaries of Mlucas 2.7c for me. Now I need some guinea pigs, er, I mean, beta testers. Thomas has built both 32-bit and 64-bit executables and verified that they run and done timings on the R10000 and R12000 systems he has access to. These are all fairly recent CPUs (i.e. they can handle 64-bit binaries) with large L2 caches. Now I need to try the code out on some older and smaller-cache systems. If you have access to an SGI which is either pre-R10000 or an R10000 with an L2 cache of 1MB or smaller and you are willing to do some tests for me, the tarball is at ftp://hogranch.com/pub/mayer/bin/SGI/Mlucas_SGI.tar.gz This contains a 32-bit and a 64-bit executable, and several .cfg files with the optimal radix combinations Thomas found on his systems. In order to run the same suite of timing tests so you can create the .cfg file optimal for your system, you'll need to also grab the source tarball: ftp://hogranch.com/pub/mayer/Mlucas_2.7c.tar.gz This tarball contains a timings.txt file, which has a complete set of entry fileds for doing benchmarks. If your system is pre-R10000, you only need do runs up to an FFT length of 1024K, unless you're curious and willing to burn the CPU time that will be needed to do the larger runlengths. I'll need answers to the following questions: 1) What type of system did you do benchmarks on? ('hinv' will give CPU and cache info; 'uname -a' should tell you which OS.) 2) Did both the 32-bit and 64-bit binaries run on your system? If yes, which is faster? 3) For the faster of the 2 binaries, a .cfg file with the optimal radix set index for each FFT length, and the table of per-iteration timings for all radix sets you tried for each FFT length. Please send these data in simple plaintext mode. Thanks in advance, - -Ernst _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Fri, 30 Nov 2001 23:04:17 +0100 From: =?utf-8?Q?Torben_Schl=C3=BCntz?= Subject: Mersenne: I have a RISC/6000 with AIX 3.1 installed This might run anything; but I'm probably to stupid to manage to set up anything on it. :-/ Can anyone use this machine as is for any purpose related offcourse to primechruncing? br tsc _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 1 Dec 2001 09:25:16 -0600 (CST) From: Warut Roonguthai Subject: Mersenne: M#39 news! http://www.academicpress.com/inscight/11302001/grapha.htm _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 01 Dec 2001 17:47:10 +0100 From: Alexander Kruppa Subject: Re: Mersenne: M#39 news! Warut Roonguthai wrote: > > http://www.academicpress.com/inscight/11302001/grapha.htm > Look like the cat is out of the bag now - it's 2^13,466,917 - 1. Was this early publication indended? I thought the press release was due only after the independent double check completed, but then they quote Tim Cusak of Entropia, which makes it sound like an official announcement. Or is the official double check finished already? Alex _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 01 Dec 2001 12:04:44 -0500 From: Jud McCranie Subject: Re: Mersenne: M#39 news! At 05:47 PM 12/1/2001 +0100, Alexander Kruppa wrote: Look like the cat is out of the bag now - it's 2^13,466,917 - 1. Was >this early publication indended? I thought the press release was due >only after the independent double check completed, but then they quote >Tim Cusak of Entropia, which makes it sound like an official >announcement. Or is the official double check finished already? The independent check was supposed to be completed today, so maybe it was. +---------------------------------------------------------+ | Jud McCranie | | | | Programming Achieved with Structure, Clarity, And Logic | +---------------------------------------------------------+ _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 1 Dec 2001 12:33:11 -0500 From: John Bafford Subject: Re: Mersenne: M#39 news! It looks to me like someone goofed in publishing this, for a few reasons. The article consistently gets the definition of Mersenne numbers wrong. While it does mention something about the expoential "2p", it claims that Mersenne numbers are of the form "2p - 1", that the previous Mersenne prime was "26,972,593 - 1", and the new one is "213,466,917 - 1". Additionally, it doesn't bother to give the length of M39, though it does for M38, and quotes Tim Cusak as saying that he "expects the new prime to be confirmed this week by a second test on a supercomputer". This article was clearly posted before the official confirmation was completed. Also, George Woltman said in an email on the 24th that the verification would complete around Dec 6th. Just my 2 cents.. - -John >Warut Roonguthai wrote: > > http://www.academicpress.com/inscight/11302001/grapha.htm > >Look like the cat is out of the bag now - it's 2^13,466,917 - 1. Was >this early publication indended? I thought the press release was due >only after the independent double check completed, but then they quote >Tim Cusak of Entropia, which makes it sound like an official >announcement. Or is the official double check finished already? - -- John Bafford dshadow@zort.net http://www.dshadow.com/ _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 01 Dec 2001 11:03:43 -0800 From: Gerry Snyder Subject: Re: Mersenne: Re: Factoring benefit/cost ratio Steve Harris wrote: > > Actually, Richard's statement that "a 'Factored' status is better for GIMPS > than a 'Two LL' status" is not quite true. It's better for the mathematical > community as a whole, but not for GIMPS. GIMPS is looking for primes, not > factors, and without skipping over any. Hmmm, I must be having a senior moment. I would swear George said that one way a person could lose credit for a correct LL test is if later factoring finds a factor. Is my feeble brain making this up, or is finding a factor more important than stated above? Gerry - -- mailto:gerrysnyder@mediaone.net Gerry Snyder, AIS Director & Symposium Chair, Region 15 RVP Member San Fernando Valley, Southern California Iris Societies in warm, winterless Los Angeles--USDA 9b-ish, Sunset 18-19 my work: helping generate data for: http://galileo.jpl.nasa.gov/ _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 01 Dec 2001 13:01:01 -0500 From: Nathan Russell Subject: Re: Mersenne: M#39 news! At 12:33 PM 12/1/2001 -0500, John Bafford wrote: >It looks to me like someone goofed in publishing this, for a few reasons. >The article consistently gets the definition of Mersenne numbers wrong. >While it does mention something about the expoential "2p", it claims that >Mersenne numbers are of the form "2p - 1", that the previous Mersenne >prime was "26,972,593 - 1", and the new one is "213,466,917 - 1". That could be a bad conversion from some other format to HTML. >Additionally, it doesn't bother to give the length of M39, though it does >for M38, and quotes Tim Cusak as saying that he "expects the new prime to >be confirmed this week by a second test on a supercomputer". This article >was clearly posted before the official confirmation was completed. > >Also, George Woltman said in an email on the 24th that the verification >would complete around Dec 6th. So someone managed to find, or mis-find, the exponent, possibly by speaking with Entropia. I wonder how much of a blow this is to the chance of GIMPS' getting a mention in other newspapers/sites. Nathan _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 01 Dec 2001 11:07:48 -0800 From: Gerry Snyder Subject: Re: Mersenne: M#39 news! John Bafford wrote: > > It looks to me like someone goofed in publishing this, for a few > reasons. The article consistently gets the definition of Mersenne > numbers wrong. While it does mention something about the expoential > "2p", it claims that Mersenne numbers are of the form "2p - 1", that > the previous Mersenne prime was "26,972,593 - 1", and the new one is > "213,466,917 - 1". > Typesetting error, I think. In each case the contiguous numbers after the initial "2" are supposed to be the exponent. Gerry - -- mailto:gerrysnyder@mediaone.net Gerry Snyder, AIS Director & Symposium Chair, Region 15 RVP Member San Fernando Valley, Southern California Iris Societies in warm, winterless Los Angeles--USDA 9b-ish, Sunset 18-19 my work: helping generate data for: http://galileo.jpl.nasa.gov/ _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 01 Dec 2001 18:48:39 +0000 From: Gareth Randall Subject: Re: Mersenne: M#39 news! Nathan Russell wrote: > So someone managed to find, or mis-find, the exponent, possibly by > speaking with Entropia. I wonder how much of a blow this is to the > chance of GIMPS' getting a mention in other newspapers/sites. Shame it's such an amateur article too. Almost anyone on this list could have written a more exciting, more interest-evoking article than that. There's a vague reference to the science whenever there's a "gee whizz" to be had, but basically the feel of an outsider without much knowledge or interest who just wants to get that "headline" out and who cares if it screws up anyone else. I would have expected a lot better from Academic Press than that. Perhaps someone here should write a better one for publication on the GIMPS website? (I can't as I'm on business for the next week, and by then it'll presumably be old news.) Yours, - -- ======= Gareth Randall ======= _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 1 Dec 2001 14:54:34 EST From: Farringr@aol.com Subject: Re: Mersenne: M#39 news! I thought it was a bit nasty in the last paragraph. The author doesn't know why people search for Mersenne primes, so it must be stupid. Check the attributions, it was written by someone at Science News. http://sciencenow.sciencemag.org/ Bob Farrington 12/1/2001 10:53:47 AM PST, gareth.randall@virgin.net writes: Nathan Russell wrote: > So someone managed to find, or mis-find, the exponent, possibly by > speaking with Entropia. I wonder how much of a blow this is to the > chance of GIMPS' getting a mention in other newspapers/sites. >> Shame it's such an amateur article too. Almost anyone on this list could have written a more exciting, more interest-evoking article than that. There's a vague reference to the science whenever there's a "gee whizz" to be had, but basically the feel of an outsider without much knowledge or interest who just wants to get that "headline" out and who cares if it screws up anyone else. I would have expected a lot better from Academic Press than that. Perhaps someone here should write a better one for publication on the GIMPS website? (I can't as I'm on business for the next week, and by then it'll presumably be old news.) << _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 1 Dec 2001 20:02:52 -0000 From: bjb@bbhvig.uklinux.net Subject: Re: Mersenne: M#39 news! On 1 Dec 2001, at 17:47, Alexander Kruppa wrote: > Warut Roonguthai wrote: > > > > http://www.academicpress.com/inscight/11302001/grapha.htm > > > > Look like the cat is out of the bag now - it's 2^13,466,917 - 1. Was > this early publication indended? I thought the press release was due > only after the independent double check completed, but then they quote > Tim Cusak of Entropia, which makes it sound like an official > announcement. Or is the official double check finished already? Umm. If this is true I'm _very_ annoyed about the leakage. My hope is that it _isn't_ true that the exponent is 13466917. "Official" supporting evidence is admittedly thin, but that Mersenne number has 4,053,946 digits - if that was true, I would have expected George's initial announcement to say "over 4 million digits" rather than "well over 3.5 million digits" (which would nevertheless be true!). Of course I could simply be misreading George's mind - possibly if he had said "over 4 million" it would have narrowed the field sufficiently to make identification easy. But is it _really_ too much to ask people to wait just one more week for the official verification run to complete? Maths isn't like politics, what's true today won't be different tomorrow... I would strongly suggest that procedures are changed so that the next time a Mersenne prime is discovered, no information at all is released except to prior discoverers of Mersenne primes and any others (at George's discretion) who might be in a position to do the official verification run. Incidentally I did reply to a request for information about M39 which appeared on the NMBRTHRY list yesterday morning. I was very, very careful to include no information which has not been released by George in his messages to this list, and I made sure George got a copy of my reply. Irritated Brian Beesley _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 1 Dec 2001 22:38:28 +0100 From: =?utf-8?Q?Torben_Schl=C3=BCntz?= Subject: SV: Mersenne: I have a RISC/6000 with AIX 3.1 installed > This might run anything; but I'm probably to stupid to manage to set > up anything on it. :-/ Can anyone use this machine as is for any > purpose related offcourse to primechruncing? If the system has a C compiler, you can certainly run LL tests using Glucas. No C compiler; not even man-pages. But some cute system called SMIT which can do quite many things. :-) Building Glucas is dead easy. If you don't have a C compiler, you can almost certainly install gcc, though this is more complicated and a lot more work than building Glucas. In any case you would probably find a R6000 AIX binary version of Glucas if you asked, or someone out there with a similar system who would build one for you. I go for both; Does any one has a glucas binary for RISC/6000 AIX? I don't know how fast the system might be, but there is plenty of work even for slower systems. I believe it to be 300 Mhz; And it was at least once some kind of a "mainframe". BTW I got it for only $ 15! And _yes_ I got slow machines (an -486 80 mhz requering appr. 9 months to complete a 65 bit factoring). Best regards Torben Schlntz _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 01 Dec 2001 17:39:39 -0500 From: George Woltman Subject: Re: Mersenne: Re: Factoring benefit/cost ratio Hi Gerry, At 11:03 AM 12/1/2001 -0800, Gerry Snyder wrote: >I must be having a senior moment. I would swear George said that one way >a person could lose credit for a correct LL test is if later factoring >finds a factor. This is because my rather limited reporting software only adds up the LL results in the verified and one-LL-tests databases. Once an exponent is factored it is removed from those databases. >Is my feeble brain making this up, or is finding a factor more important >than stated above? I prefer a factor to a double-check. But it is hard to quantify "prefer" in a mathematical formula for computing trial factoring limits. Prime95 uses the formula: cost_of_factoring must be less than chance_of_finding_a_factor times 2.03 * the cost_of_an_LL_test. This should maximize GIMPS throughput. The 2.03 is because we must run two (or more) LL tests to do a double-check. - -- George P.S. I'll comment on the M#39 news later. For now lets celebrate our grand accomplishment rather than worry about non-optimal press coverage. _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sat, 1 Dec 2001 19:32:34 -0600 From: "Steve Harris" Subject: Re: Mersenne: Re: Factoring benefit/cost ratio George did say that, and I was aware of his statement, but that still has no effect on the point I was making. George's GIMPS stats also give no credit at all for finding factors, but that doesn't mean he considers finding factors worthless. Steve - -----Original Message----- From: Gerry Snyder To: mer Date: Saturday, December 01, 2001 12:19 PM Subject: Re: Mersenne: Re: Factoring benefit/cost ratio >Steve Harris wrote: >> >> Actually, Richard's statement that "a 'Factored' status is better for GIMPS >> than a 'Two LL' status" is not quite true. It's better for the mathematical >> community as a whole, but not for GIMPS. GIMPS is looking for primes, not >> factors, and without skipping over any. > >Hmmm, > >I must be having a senior moment. I would swear George said that one way >a person could lose credit for a correct LL test is if later factoring >finds a factor. > >Is my feeble brain making this up, or is finding a factor more important >than stated above? > >Gerry >-- >mailto:gerrysnyder@mediaone.net >Gerry Snyder, AIS Director & Symposium Chair, Region 15 RVP >Member San Fernando Valley, Southern California Iris Societies >in warm, winterless Los Angeles--USDA 9b-ish, Sunset 18-19 >my work: helping generate data for: http://galileo.jpl.nasa.gov/ >_________________________________________________________________________ >Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm >Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers ------------------------------ Date: Sun, 2 Dec 2001 18:55:57 -0000 From: bjb@bbhvig.uklinux.net Subject: Re: Mersenne: Re: Factoring benefit/cost ratio On 1 Dec 2001, at 17:39, George Woltman wrote: > This is because my rather limited reporting software only adds up the > LL results in the verified and one-LL-tests databases. Once an > exponent is factored it is removed from those databases. The other problem here is that the "known factors" database does not include the discoverer. > > I prefer a factor to a double-check. But it is hard to quantify > "prefer" in a mathematical formula for computing trial factoring > limits. Prime95 uses the formula: cost_of_factoring must be less > than chance_of_finding_a_factor times 2.03 * the cost_of_an_LL_test. > > This should maximize GIMPS throughput. The 2.03 is because we must > run two (or more) LL tests to do a double-check. Again there is a complication, since the ratio of time to do factoring assignment X to time to do LL/DC assignment Y varies according to the processor. e.g. PIIs are relatively quick at factoring, whereas P4s are much more efficient LL testers. > > P.S. I'll comment on the M#39 news later. For now lets celebrate our > grand accomplishment rather than worry about non-optimal press > coverage. Hear hear. Congratulations to the discoverer (whoever he/she is), to George on his program finding a fifth Mersenne Prime, and to everyone involved in the project, without whom we wouldn't have reached this milestone. Regards Brian Beesley _________________________________________________________________________ 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 #912 ******************************