From wedgingt Sat Feb 24 22:17:33 1996 From: "George F. Woltman" <74473.2626@compuserve.com> Subject: Mersenne Prime Search Date: 24 Feb 96 21:18:21 EST Hello Mersenne Searchers, Enclosed is a newsletter to keep everyone up-to-date during the long, lonely search for Mersenne primes. Please let me know if you have any suggestions or would like your name removed from my mailing list. Many Thanks, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #1 February 24, 1996 Status ------ Since launching the search in early January, many of the lower ranges have been completed with no new Mersenne primes found. We now have over 40 people and over 50 computers involved in the search. In January, there were over 24,000 primes under 1,000,000 that needed checking. Today there are now less than 21,000. Well done! David Slowinski --------------- As most of you know, David Slowinski has been searching for Mersenne primes for 17 years using spare CPU cycles on his company's supercomputers. Unfortunately, he has not shared any information on the primes he has already tested. However, he did offer to verify the residues of a dozen primes to make sure our Lucas-Lehmer test program is operating correctly. He verified the residues for: 659077, 659101, 659173, 710207, 945151, 950617, 973289, 979691, 981023, 989477. He had not tested: 719027, 732041 >From this I concluded two things. One, there are indeed untested ranges below 859433. Two, Mr. Slowinski has probably tested most of the primes from 859,433 to 1,000,000 or more in an effort to find a new record. As a result, I've opened up the ranges from 1000 to 1299 for searching. If you want to find a new world record prime and have checked out a range between 860 and 1000, I would suggest you pick a range above 1100. Just mail me the results that you have already and the new range you'd like to test. You'll also need to download the latest program and database to test these new ranges. What are the odds? ------------------ I'm often asked "What are my chances of finding a Mersenne prime?" Should you be lucky enough to pick a range that David Slowinski has not previously tested - the following table approximates your chances: Prime Odds for one Lucas-Lehmer test Odds for an entire range ------ ------------------------------ ------------------------ 400000 1 in 4000 about 1 in 130 600000 1 in 5900 about 1 in 200 800000 1 in 7550 about 1 in 250 1000000 1 in 9250 about 1 in 300 1200000 1 in 11000 about 1 in 370 The above odds are only for primes where the program did not find a factor. Program News ------------ The factoring part of the program was originally written for 386 computers. Since 486 and Pentium machines have a floating point unit and a data cache, there are new optimizations that can be made. So far, the factoring has been improved by 30%. Since the program can now factor faster it makes sense to check for more factors before beginning a Lucas-Lehmer test. This will improve the overall time spent testing a range by about 2%. This new version of the program is now available on the Web. By the way, if you're worried that your 486 cannot run Lucas-Lehmer tests in a timely manner, you can now use your 486 for factoring only. See the web pages for more details. Happy Hunting, George Woltman
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From wedgingt Mon Feb 26 21:02:00 1996 From: "George F. Woltman" <74473.2626@compuserve.com> Subject: Mersenne Prime Search Date: 26 Feb 96 20:43:45 EST Hello Mersenne Searchers, I'm sorry to bother everyone so soon after my last newsletter, but I thought a special edition was warranted. Regards, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #2 February 26, 1996 SPECIAL EDITION Status ------ Peter Marksteiner spent a couple of years running Lucas-Lehmer tests on most of the untested primes between 200000 and 471000. Although his program did not keep residues, he has modified it do so. We are now verifying the program by re-running some of the tests and comparing residues. So far, so good. As a result, instead of 30,469 there are now just 26,997 primes under 1,300,000 left to test. The databases on the web have been updated accordingly. For those of you currently testing a range between 355 and 471, I'd recommend you send your results thusfar (so that we have residues), delete any intermediate files (pNNNNNNN), download the latest db2.zip database, and select a new range. Happy hunting, George Woltman P.S. No new Mersenne primes were found.
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From wedgingt Sat Apr 13 11:05:49 1996 From: "George F. Woltman" <74473.2626@CompuServe.COM> Subject: Mersenne Newsletter #3 Date: 12 Apr 96 15:55:19 EDT Hello Mersenne Searchers, Enclosed is newsletter #3 to keep everyone up-to-date during the long search for Mersenne primes. Please let me know if you have any suggestions or would like your name removed from my mailing list. Many Thanks, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #3 April 12, 1996 Welcome ------- Since the last newsletter 45 days ago, we've added 35 new members to our ranks. This brings to more than 75 people and 90 computers involved in the search. Welcome to all the new searchers! Status ------ Also over the past 45 days, we've proven 1,389 Mersenne numbers composite. This leaves us with "only" 25,608 untested Mersenne numbers with exponents below 1,300,000. If you use a 90 MHz Pentium as a standard, these 25,608 numbers can be tested in just over 129 CPU years. Keep those results rolling in! Someone is bound to find a Mersenne prime sooner or later! Program News ------------ A new version of the program has been placed on the web. You can download it from http://ourworld.compuserve.com/homepages/justforfun/prime.htm. I recommend everyone upgrade to this version at their ealiest convenience. Some highlights of the new version: Thanks to Albert van der Horst and Richard Hibberd the program no longer crashes in Windows 3.1!!! You can now work in other Windows applications while prime.exe is running! Rather than a simple test of 2^19937-1, the program will now perform an hour long self-test of many different exponents. This should catch any machine not capable of running Lucas-Lehmer tests. You can now get a status report on your range. Choose Range Status from the menus to get a report on the number of Mersenne numbers left to test, expected time to completion, etc. This information is also displayed whenever you choose a new range with Range Start or Range Next. Factoring speed has been doubled for Pentiums. 486 machines will notice a 15% improvement when factoring. As always, comments and suggestions for future enhancements are welcome. Happy hunting, George Woltman 74473.2626@compuserve.com
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From wedgingt Wed Jun 12 01:18:47 1996 From: "George F. Woltman" <74473.2626@CompuServe.COM> Subject: Mersenne Newsletter #4 Date: 11 Jun 96 20:38:01 EDT Hello Mersenne Searchers, Enclosed is newsletter #4 to keep everyone up-to-date during the long search for Mersenne primes. Please let me know if you have any suggestions or would like your name removed from my mailing list. If you've stopped searching, please send any results you may have and let me know so that others can finish testing your range. Many Thanks, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #4 June 11, 1996 Welcome ------- Since the last newsletter 60 days ago, we've added 50 new members to our ranks. This brings to more than 140 people and an estimated 170+ computers involved in the search. Welcome to all the new searchers! Status ------ Also over the past 60 days, we've proven a whopping 3,743 Mersenne numbers composite! This leaves us with only 21,865 untested Mersenne numbers with exponents below 1,300,000. If you use a 90 MHz Pentium as a standard, these numbers can be tested in just over 103 CPU years. For those that would like a breakdown, here are the number of exponents that need testing in each 100,000 range: 300000-400000 49 400000-500000 357 500000-600000 2084 600000-700000 2625 700000-800000 3030 800000-900000 2891 900000-1000000 2760 1000000-1100000 3040 1100000-1200000 2819 1200000-1300000 2210 We're making such good progress that I opened up the exponents from 1,300,000 to 2,630,000 for testing! This should keep us busy well into the next century. Furthermore, 486 users have double-checked most of the Mersenne exponents below 140,000. Thanks ------ Many thanks to Luther Welsh for organizing the Mersenne mailing list. There have been several interesting discussions on various topics related to the mathematics of Mersenne numbers as well as the computer algorithms that deal with them. If interested, check it out at http://www.scruznet.com/~luke/signup.htm. Program News ------------ On May 22, a new version of the program was placed on the web. The most important new features of this version are a 10% speed increase in running Lucas-Lehmer tests and more error checking to insure accurate results! You can download the program from http://ourworld.compuserve.com/homepages/justforfun/freesoft.htm. I recommend everyone upgrade to this version at their earliest convenience. On June 11, a minor update was made to the Windows 95 version. This version allows you to run the program for a specified amount of time. It also lets you pick a different priority to run the program. As always, comments and suggestions for future enhancements are welcome. Happy hunting, George Woltman 74473.2626@compuserve.com
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From wedgingt Thu Aug 1 08:38:37 1996 From: "George F. Woltman" <74473.2626@CompuServe.COM> Subject: Mersenne Newsletter #5 Date: 31 Jul 96 21:27:14 EDT Hello Mersenne Searchers, Enclosed is newsletter #5 to keep everyone up-to-date in the search for Mersenne primes. Please let me know if you have any suggestions or would like your name removed from my mailing list. If you've stopped searching, please send any results you may have and let me know so that others can finish testing your range. Many Thanks, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #5 July 31, 1996 Welcome ------- Since the last newsletter 50 days ago, we've more than doubled our ranks! There are now more than 280 people involved in the search. Welcome to all the new searchers! Status ------ The last 50 days has also seen great progress in our search. We've proven a whopping 4,796 Mersenne numbers composite! This leaves us with only 17,603 untested Mersenne numbers with exponents below 1,300,000 and 57,424 below 2,630,000. If you use a 90 MHz Pentium as a standard, all of these numbers can be tested in 1,146 CPU years. For those that would like a breakdown, here are the number of exponents that need testing in each 100,000 range as compared to 50 days ago. 300000-400000 18 vs. 49 400000-500000 229 vs. 357 500000-600000 1067 vs. 2084 600000-700000 1243 vs. 2625 700000-800000 2663 vs. 3030 800000-900000 2670 vs. 2891 900000-1000000 2677 vs. 2760 1000000-1100000 2889 vs. 3040 1100000-1200000 2427 vs. 2819 1200000-1300000 1720 vs. 2210 Factoring --------- Brian Beuning and Torbjorn Granlund used 100 SPARC machines over 6 months to factor Mersenne numbers. Their work gave us over 2000 previously unknown factors. Thanks! I'd also like to thank Conrad Walter Curry and Will Edgington. Each has dozens of computers working at finding even more new factors. Double-checking --------------- Thanks to the "Amdahl 6" and David Slowinski for supplying residues to aid in the double-checking process. This is extremely important to be absolutely sure that a Mersenne prime hasn't gone unnoticed due to an errant Lucas-Lehmer test. Errors during Lucas-Lehmer tests are not that uncommon. Over 100 have been found already. I'm sure everyone is curious about the famous Slowinski gaps. Over 200 of the residues sent to Slowinski for verification had never been tested before. Interim Goals ------------- I have two realistic goals for the next 6 months. 1) Show that M756839 is the 32nd (or 33rd!) Mersenne prime. 2) Double-check every exponent below 400,000. All the ranges below M756839 are currently being tested. Some are being tested by 486s so they may take a while to complete. To complete the second goal, we'll need 486 owners and UNIX owners that are running Crandall's lucas.c to test less than 2,000 exponents. Pentium owners should continue testing large exponents so that 486 users have useful work to do -- it just takes too long for a 486 to test a large exponent. Program News ------------ The program has been ported for use on 486 and Pentium Linux systems. There are also Windows screen saver versions available (only recommended for Windows 3.1 and for some reason only works on half the machines that have tried it). Jason Kline has improved Crandall's lucas.c. This version can be up to twice as fast as lucas.c. You can download this version from http://www.scruznet.com/~luke/freeware.htm. Others are working on even faster versions! As always, comments and suggestions for future program enhancements are welcome. Happy hunting, George Woltman 74473.2626@compuserve.com
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From wedgingt Tue Sep 3 08:22:15 1996 From: "George F. Woltman" <74473.2626@CompuServe.COM> Subject: New Mersenne Prime! Date: 03 Sep 96 09:13:31 EDT The Mersenne Newsletter, issue #6 September 3, 1996 New Mersenne Prime! ------------------- Congratulations go to David Slowinski and Paul Gage. In early April, they discovered the 34th known Mersenne prime: 2^1257787-1. The find took 6 hours on a Cray supercomputer. You can read all about it in the San Jose Mercury News, http://www.sjmercury.com/business/compute/prime.htm or the Silicon Graphics web page, http://reality.sgi.com/csp/ioccc/noll/prime/prime_press.html At David's request, the find was not announced until today. On April 15, David asked me to verify his new find. Ironicly, at the time I received his email, my own Pentium-90 was 95% of the way through testing that exponent. That hurt for a few days! However, I also saw a lot of positives. Despite a two-year head start, David found the new prime only a few days before we did. Furthermore, our effort was just getting under way, we now have more than 4 times as many searchers as we did then. I firmly believe that the 35th Mersenne prime will be found by a member of our group! I have but one regret: After picking the lucky 1257 range, I wish I had run it on my Pentium Pro 200 instead of the Pentium-90! Our group has made great progress since April in closing the gaps left by David and in searching the new territory above 1257787. Keep up the good work! Best wishes and Good luck, George Woltman woltman@magicnet.net
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From wedgingt Sat Nov 2 11:23:02 1996 From: "George F. Woltman" <74473.2626@CompuServe.COM> Subject: Mersenne Newsletter #7 Date: 01 Nov 96 21:44:00 EST Hello Mersenne Searchers, Enclosed is newsletter #7 to keep everyone up-to-date in the search for Mersenne primes. Please let me know if you have any suggestions or would like your name removed from my mailing list. If you've stopped searching, please send any results you may have and let me know so that others can finish testing your range. Many Thanks to Everyone, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #7 November 1, 1996 Welcome ------- Since the last full newsletter 3 months ago, the number of searchers has skyrocketed! There are now 720 people involved compared to 280 three months ago. Welcome to all the new searchers! Big Program News ---------------- Version 13 of the Pentium Lucas-Lehmer test program is now available. It is a *lot* faster on exponents above 675,000. The Lucas-Lehmer assembly code was almost completely rewritten to increase modularity and readability. This also reduced L2 cache activity which can speed up the Lucas-Lehmer test by up to 10%. I also added a little bit of PFA (Prime Factor Algorithm FFT). Where the old code supported FFT sizes of 64K and 128K, the new code supports 64K, 80K, 96K, 112K, and 128K. Here are the iteration timings I get with the old and new version. Exponent CPU old code new code savings 675,000-1,330,000 Pro200 0.072 0.072 0% 1,330,000-1,675,000 Pro200 0.159 0.096 40% 1,675,000-2,000,000 Pro200 0.159 0.117 27% 2,000,000-2,330,000 Pro200 0.159 0.142 11% 2,330,000-2,630,000 Pro200 0.159 0.159 0% 675,000-1,330,000 P90 0.177 0.165 7% 1,330,000-1,675,000 P90 0.426 0.227 47% 1,675,000-2,000,000 P90 0.426 0.272 36% 2,000,000-2,330,000 P90 0.426 0.332 22% 2,330,000-2,630,000 P90 0.426 0.371 13% The new program is SLOWER on exponents below 675,000. I strongly encourage all users testing exponents above 675,000 to download the new program. Follow the easy steps below. 1) Go to http://ourworld.compuserve.com/homepages/justforfun/freesoft.htm. Download either prime.zip, prime95.zip, or mprime.tgz. 2) Unzip the new version on top of the old version. 3) Run the new program and choose Range / Continue. 4) You will be required to run a new one-hour self-test. This will happen automatically. You do not need to run the 5 hour self-test from the Options / Self-test choice. 5) You do not need to download a new database. You can install the new version even if you're in the middle of testing an exponent. A side note - when the new program continues a Lucas-Lehmer test started by the previous version, it will not use the smaller length FFT. When the new version starts the next exponent in your range you'll get the full benefit of the smaller FFT run length. Status and New Goals -------------------- The last three months has seen great progress in our search. We've proven over 11,000 Mersenne numbers composite! There are no untested exponents below 559,000 and only a few hundred exponents left to test below 756,839. This progress cut our Pentium-90 estimate to 1020 CPU years. The new program reduces this estimate to 777 CPU-years to test all 46,501 remaining exponents below 2,655,000. I've also adjusted our goals slightly. I now hope to test all exponents below 1,345,000 by the end of 1997 and all exponents below 2,655,000 by the year 2000. This minor change is related to the new program's ability to test more exponents in a given FFT run length. Source code ----------- Source code is now available on the net! Download source.zip from my "Source code!" page. PowerMac -------- John Sweeney has taken many of my FFT tricks and put them in a C program that runs on PowerMac PCs. His program has excellent performance. You can download his program from my "Free Software!" web page. This was a tremendous undertaking by John. Thanks! Miscellaneous ------------- If you've sent any results to me, then your name should appear on my "Credits" web page. If I have forgotten, misspelled, or misalphabetized your name, then please let me know. By the way, I now know how to add accents and umlauts so check that too. The web site now has a spiffier status page (thanks Luke) and a top fifty producers page. I sent 6,000 residues to David Slowinski for verification. Of the 5,000 he was able to verify, there were fewer than 50 mismatches. This amount to a COMBINED error rate of less than 1%! This is excellent! I'm swamped! I'm not complaining. Managing 700+ testers takes a fair amount of time. Until I can write a few programs to automate my work, here's a couple little things you can do to lighten my load. Only send results once a month or when your range ends. Daily or weekly email adds to my overhead. After sending results place a "marker" in the results file indicating results after this point are new results. I know this may not be feasible for those of you running the program on several machines - that's OK. Of course, if you find a new Mersenne prime, send that right away :-) Best wishes to all, George Woltman woltman@magicnet.net
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From wedgingt Sat Nov 23 08:57:57 1996 From: "George F. Woltman" <74473.2626@CompuServe.COM> To: BlindCopyReceiver:;@compuserve.com Subject: New Mersenne Prime! Date: 23 Nov 96 09:42:40 EST The Mersenne Newsletter, issue #8 November 23, 1996 New Mersenne Prime! 2^1398269-1 is prime! ------------------------------------------ Thanks to everyone's hard work, GIMPS (Great Internet Mersenne Prime Search) has discovered the 35th known Mersenne Prime! Joel Armengaud made the discovery on November 13. Amazingly, he kept this secret while he double-checked the find on two other computers. On the 18th, he notified Richard Crandall, Chris Caldwell, and myself. I verified it on my machine on the 20th. Slowinski, who was out of town at the time, provided the independent verification on the 22nd. More information can be found at these three web sites: http://www.sjmercury.com/business/compute/prime1122.htm http://ourworld.compuserve.com/homepages/justforfun/1398269.htm http://www.utm.edu/research/primes/notes/1398269.html As had been agreed upon before hand, credit for this new prime will go to Armengaud, Woltman, et. al. We were incredibly lucky to find this prime. In percentage terms, this is the 6th smallest gap between Mersenne exponents. The range from 1,000,000 to 2,000,000 was expected to contain 1.78 Mersenne primes. There are already 2 known and probablities suggest there will be one more. Let's go find that one too! Congratulations to all, George Woltman woltman@magicnet.net
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From wedgingt Thu Jan 16 10:02:35 1997 From: "George F. Woltman" <74473.2626@CompuServe.COM> To: BlindCopyReceiver:;@compuserve.com Subject: Mersenne Newsletter #9 Date: 15 Jan 97 22:21:51 EST Hello Mersenne Prime Searchers, Enclosed is newsletter #9 to keep everyone up-to-date in the search for Mersenne primes. Please let me know if you have any suggestions or would like your name removed from my mailing list. If you've stopped searching, please send any results you may have and let me know so that others can finish testing your range. Many Thanks to Everyone, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #9 January 15, 1996 M756839 is the 32nd Mersenne Prime ---------------------------------- Today, the last few Lucas-Lehmer results below 756839 trickled in. Congratulations and thanks to all who contributed in "proving" this is the 32nd Mersenne. For those that are nit-pickers, you may be wondering what is the chance that there was an error in our calculations and a Mersenne prime escaped discovery. There are roughly 1230 exponents that have only been checked once, but not all of these have been sent to David Slowinski for verification. Assuming he will verify about half of these and assuming an error rate of 1%, then the chance of a missed Mersenne prime is less than 1 in a 1000. Happy Anniversary ----------------- The Great Internet Mersenne Prime Search is now one year old. The first searcher, Reuven Singer, joined the first week in January. Luke Welsh, who coined GIMPS, joined shortly thereafter. On January 21, we posted an invitation to sci.math. I had hoped to gather 100 searchers to test all the exponents below 1,000,000 by 1999. I sure did underestimate the response! It has been a pleasure working with all of you. Thanks. Welcome ------- Since the last full newsletter 2 and a half months ago, the number of searchers has swelled to 1150 - an increase of 430! Welcome to all the new searchers! New Web Address --------------- In case you haven't noticed, the web pages have moved to http://www.mersenne.org/prime.htm. This is much easier to remember than the previous Compuserve address. Many thanks to Jeff Woods for hosting the web pages. Program News ------------ Not much has happened since Version 13 was released in early November. A few bugs have been fixed and there is now a version that can run as a Windows NT service. I've modified the error checking that is done every iteration. The new test should catch more hardware errors and thus increase the reliability of our results. This new code is presently being tested in the Linux version. I am well aware that we are running out of ranges to test. Who would have imagined that? I am working on code that will allow testing exponents up to roughly 5,300,000. Status ------ Since the beginning of November, we've proved 14,573 Mersenne numbers composite (and one prime). There are 31,927 exponents remaining below 2,655,000. The Pentium-90 CPU years estimate dropped to 624 from 777. PowerMac -------- John Sweeney has continued to improve his C code. If you're not running version 1.4 please upgrade as soon as possible. Miscellaneous ------------- I now have a program to help me process results files. Duplicate results and results that are not in sorted order are no longer a problem. There is a small group working on automatically checking out ranges and reporting results to a server on the Internet. The present manual system will still be available, but this new method will be easier for me and for those of you managing multiple machines. Email is not the most efficient way to manage a project of this size. Hopefully, we'll have everything in place by summer. Best wishes to all, George Woltman woltman@magicnet.net
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From: George Woltman <woltman@magicnet.net> To: (Recipient list suppressed) Subject: Mersenne Newsletter #10 Date: Thu, 13 Mar 1997 14:49:59 -0500 Hello Mersenne Prime Searchers, Enclosed is newsletter #10 to keep you up-to-date in our search for Mersenne primes. Please let me know if you would like your name removed from my mailing list. If you've stopped searching, please send any results you may have and let me know so that others can finish testing your range. Many Thanks to Everyone, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #10 March 11, 1996 New email address ----------------- Due to sluggish performance on Compuserve, I've decided to make woltman@magicnet.net my only email account. Many of you are already using this address. Please update your records accordingly. I hope to close the Compuserve account by the end of this year. Program News ------------ Version 14 was released on March 3rd. This program can test larger exponents and has improved error checking. Factoring on Pentium computers is slightly faster. This version is backward compatible with the previous version. If you've ever had a FATAL ERROR, I strongly recommend downloading the new version. I recommend everyone else upgrade to the new version if it is easy to do so. New Ranges! ----------- The exponents from 2,655,000 to 5,260,000 are now available for testing! You could become the first person to discover a million digit prime number! Chris Caldwell, http://www.utm.edu/research/primes/notes/by_year.html, projects that one won't be found until 2007. Care to beat that projection by ten years? Just find a Mersenne prime with an exponent above 3,321,927. Lennart Grebelius' web page, http://www2.tripnet.se/~nlg/mersenne/benchmk.htm, will give you an idea how long these exponents take to test. The Small Ranges are Gone! -------------------------- All ranges below 2,655,000 are now checked out! If you have checked out much more than a three month supply of exponents, please email me so we can trim your range down and let others test the remainder. Status ------ Since mid-January, we've proved 10,204 Mersenne numbers composite. There are 21,723 exponents remaining below 2,655,000. The Pentium-90 CPU years estimate dropped to 460 from 624. In the new range from 2,655,000 to 5,260,000, there are 82,033 exponents to test. It will take an estimated 6,841 P-90 CPU years to complete. Best wishes to all, George Woltman woltman@magicnet.net
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From: George Woltman <woltman@magicnet.net> To: (Recipient list suppressed) Subject: Mersenne Newsletter #11 Date: Mon, 26 May 1997 15:45:16 -0400 Hello Mersenne Prime Searchers, Enclosed is newsletter #11 to keep you up-to-date in our search for Mersenne primes. Please let me know if you would like your name removed from my mailing list. Many Thanks to Everyone, George Woltman ---------------------------------------------------------------------- The Mersenne Newsletter, issue #11 May 26, 1997 IMPORTANT: New Range Reservation Policy --------------------------------------- In the past, I have sent email to those who have been slow in reporting results from a range they have checked out. Unfortunately, I am no longer able to do this. It is just too time consuming. Starting June 1, I will return a range to the available pool if either of the following occur: 1) No results are reported during a 4 month period. 2) The range is not completed within 8 months. Hopefully, this will not be a burden to anyone - especially since I encourage you to send in results once every month or two. As always, I can make exceptions if you let me know ahead of time. This policy will make it easier for me to detect people who have dropped out of the search and will ensure that active testers will always have the smallest possible ranges to choose from. Milestone! ---------- Two-and-a-half years ahead of my original schedule, GIMPS has completed testing all exponents below 1,000,000! Can 2,000,000 be far behind? My records indicate we are more than 94% of the way there! Status for exponents below 2,655,000 ------------------------------------ Since mid-March, we've proved another 10,936 Mersenne numbers composite. There are now only 10,787 untested exponents remaining below 2,655,000. We've been so effective at finding composites that the chance of finding a new Mersenne prime in this range has fallen to 50%. The time required to finish this range has dropped from 460 Pentium-90 CPU-years to 238. Status for exponents from 2,655,000 to 5,260,000 ------------------------------------------------ Since mid-March, we've proved 7,484 Mersenne numbers composite. Most of these composite numbers were found by people running the factoring step. Less than a 1,000 Lucas-Lehmer tests have been run in this range. There are now 74,549 exponents left to test. It will take an estimated 6,233 P-90 CPU years to complete. Best wishes and good luck to all, George Woltman woltman@magicnet.net
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From: George Woltman <woltman@magicnet.net> To: (Recipient list suppressed) Subject: Mersenne Newletter #12 - A prime has been found! Date: Mon, 01 Sep 1997 18:08:08 -0400 The Mersenne Newsletter, issue #12 September 1, 1997 36th Known Mersenne Prime Discovered!!! --------------------------------------- Congratulations to Gordon Spence. On August 24th he returned from a short trip to find his computer beeping like crazy. He turned on the monitor to find that his computer had proved 2^2976221 - 1 is prime! This prime number is a whopping 895,932 digits long. The computation took 15 days on his 100-MHz Pentium computer. David Slowinski confirmed the find on August 29th. Gordon was quite lucky. In the last "Top Producers" list, compiled on August 6th, Gordon ranked 127th with only 61 exponents tested. Congratulations and credit also go to every GIMPS searcher. It would have taken Gordon nearly a millenium to find this prime if he had been working alone. If there are no Mersenne primes between M1398269 and M2976221, then the gap between the 35th and 36th Mersenne primes will be the 4th largest in percentage terms. However, there are 8,554 exponents left to test below M2976221. You can read the official press release at http://www.mersenne.org/2976221.htm. IMPORTANT REMINDER: New Range Reservation Policy ------------------------------------------------ Ranges will be returned to the available pool if no results are reported during a 4 month period. Hopefully, this will not be a burden to anyone - especially since I encourage you to send in results once every month or two. As always, I can make exceptions if you let me know ahead of time. This policy will make it easier for me to detect people who have dropped out of the search and will ensure that active testers will always have the smallest possible ranges to choose from. More Milestones! ---------------- GIMPS has finished testing all exponents below M1257787, confirming that M1257787 is the 34th Mersenne Prime. GIMPS has now double-checked all exponents below M756839 and M859433 - definitively proving them to be the 32nd and 33rd Mersenne primes. Status for exponents below 2,655,000 ------------------------------------ Since the last newsletter on May 26th, we've proved another 6,460 Mersenne numbers composite. There are now only 4,327 untested exponents remaining below 2,655,000. The chance of finding a new Mersenne prime in this range has fallen from 50% to 22%. The time required to finish this range has dropped from 238 Pentium-90 CPU-years to 105. Status for exponents from 2,655,000 to 5,260,000 ------------------------------------------------ Since May 26th, we've proved 9,363 Mersenne numbers composite. There are now 65,186 exponents left to test. We've reduced the work effort by 578 CPU years, leaving an estimated 5,655 P-90 CPU years to complete. Best wishes and good luck. Maybe you will be the one to find the 37th Mersenne prime! George Woltman woltman@magicnet.net
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From: George Woltman <woltman@magicnet.net> To: (Recipient list suppressed) Subject: Mersenne Newsletter #13 - another record prime! Date: Tue, 03 Feb 1998 08:58:23 -0500 The Mersenne Newsletter, issue #13 February 2, 1998 37th Known Mersenne Prime Discovered!!! --------------------------------------- Congratulations to Roland Clarkson. On January 27th he discovered that 2^3021377 - 1 is prime! This prime number is 909,526 digits long. The computation took 46 days part-time on his 200-MHz Pentium computer. David Slowinski confirmed the find on January 31st. Roland is a 19 year-old sophmore at California State University Dominguez Hills. He is the third youngest Mersenne prime discoverer - behind Noll and Nickel. Incredibly, this was only the 8th exponent he has tested! Unlike the previous GIMPS finds, Roland let the PrimeNet server (see Program News below) choose the lucky exponent. At first, he did not want to test the exponent. Roland said, "I never would have imagined two Mersenne primes would be so close together!". In fact, in percentage terms, the gap between the 36th and 37th Mersenne primes is the smallest ever. To acknowledge Scott Kurowski's work on the PrimeNet server and every GIMPS participants diligent work, official credit for this prime will go to "Clarkson, Woltman, Kurowski, et.al.". You can read the official press release at http://www.mersenne.org/3021377.htm and be sure to check out Chris Caldwell's web pages starting at http://www.utm.edu/research/primes/notes/3021377/ Program News ------------ Version 15 of prime95 is now available. This version contacts a central server on the Internet to get exponents to test and report past results. We call this PrimeNet. Many thanks to Scott Kurowski who wrote all the server and client-side networking code. He also keeps the server running smoothly. PrimeNet should greatly reduce my work load so that I can write new code to let us test even larger exponents! Version 15 is only available for Windows 95 and Windows NT, but the other ports should be available in the coming weeks. The best time to upgrade is when you are within a month of finishing your current range. Just download and unzip the new prime95.exe on top of the old prime95.exe. Read the readme and whatsnew files. Run the program, answer the questions, and you're done. The new version should finish off your old range, then report results and get new exponents from the PrimeNet server! No more email!! Need another reason to upgrade? Scott is offering a cash prize if you find the 38th Mersenne Prime using PrimeNet. More Milestones! ---------------- GIMPS has finished testing all exponents below 1,800,000, confirming that M1398269 is the 35th Mersenne Prime. Status for exponents below 2,655,000 ------------------------------------ Since the last newsletter on September 1st (I apologize for the long gap between newsletters), we've proved another 3,670 Mersenne numbers composite. There are now only 657 untested exponents remaining below 2,655,000. The chance of finding a new Mersenne prime in this range has fallen from 22% to 3%. The time required to finish this range has dropped from 105 Pentium-90 CPU-years to 18. Status for exponents from 2,655,000 to 5,260,000 ------------------------------------------------ Since September 1st, we've proved 20,128 Mersenne numbers composite. There are now 45,058 exponents left to test. We've reduced the work effort by 1,348 CPU years, leaving an estimated 4,307 P-90 CPU years to complete. IMPORTANT REMINDER: Range Reservation Policy -------------------------------------------- Ranges may be returned to the available pool if no results are reported during a 4 month period. Hopefully, this will not be a burden to anyone - especially since I encourage you to send in results once every month or two. As always, I can make exceptions if you let me know ahead of time. Best wishes and good luck. Maybe you will be the one to find the 38th Mersenne prime! It could be over a million digits long. George Woltman woltman@magicnet.net
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From woltman@magicnet.net Fri May 22 09:03:25 1998
From: George Woltman <woltman@magicnet.net>
To: (Recipient list suppressed)
Subject: Mersenne Newsletter #14
Date: Fri, 22 May 1998 11:09:32 -0400
The Mersenne Newsletter, issue #14 May 22, 1998
IMPORTANT! Version 16 of the program released
---------------------------------------------
We are running out of exponents to test below 5,260,000!! There is
less than a two week supply of exponents to assign.
Please download version 16 of the program, it can test exponents
as high as 20,500,000. If you are running version 14 of the program,
you can wait until your current range completes before upgrading. If
you are upgrading from version 15, follow these simple steps:
1) Download the new version.
2) If the program needs to contact the server (a prime.spl file
is present in the directory), then let the old version report
these spooled results.
3) Install the new version on top of the old version.
(If you renamed HttpNet.dll to PrimeNet.dll for version 15,
then rename the file again for version 16. If you use a proxy
server userid/password in the primenet.ini file, you must
set ProxyMask=0 and re-enter the password in the file.)
4) Start the program. Optionally read the whatsnew.txt file to
see what new features are available.
GIMPS is now almost entirely automated on the PrimeNet server.
You can watch the hourly progress of the search on the server's
status page at http://entropia.com/primenet/status.shtml. News on
distributed computing aspects of automating GIMPS, new software
availability and related information is also there.
Manual testing "ranges" should be acquired from PrimeNet. Click
the link at the top of the status page, and use the simple web
forms to get exponents and check in your test results. The forms
accept results from Prime95/NTPrime (versions 16.3, 15.4, 14.4),
MacLucas V1.4, MPrime V15.4 and V16.3, and PRIMEOS2 V3.0 programs.
The most frequently asked questions and answers about using Prime95
and NTPrime with PrimeNet are also linked at the top of the status
page. If your question is not covered, network problems or PrimeNet
account issues can be sent to Scott Kurowski, primenet@entropia.com.
The PrimeNet status page highlights how quickly exponents below
5,260,000 are disappearing. Fortunately, version 16 should keep our
computers busy for years to come!
Status for exponents below 2,655,000
------------------------------------
Since the last newsletter on February 2, the number of untested
exponents has dropped from 657 to 116, with only a 1% chance of
finding a new Mersenne prime.
Status for exponents from 2,655,000 to 5,260,000
------------------------------------------------
Since February 2, we've proved 20,370 Mersenne numbers composite.
There are now 24,688 exponents left to test. We've reduced the
work effort by 1,752 CPU years, leaving an estimated 2,555 P-90 CPU
years to complete.
IMPORTANT REMINDER: Policy on Manually Reserved Ranges
------------------------------------------------------
Ranges may be returned to the available pool if no results
are reported during a 4 month period.
Best wishes and good luck. Maybe you will be the one to find
the 38th Mersenne prime!
George Woltman
woltman@magicnet.net
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From woltman@alum.mit.edu Sun Apr 4 18:09:48 1999
From: "George Woltman" <woltman@alum.mit.edu>
To: <wedgingt@acm.org>
Subject: The Mersenne Newsletter, issue #15
Date: 05 Apr 99 01:15:29 +-0100
To: Great Internet Mersenne Prime Search Registered Recipient
Note: This will be the last automatically emailed newsletter. You
will not receive anymore newsletters unless you explicitly sign up
as described below.
VERY IMPORTANT: Please read this if you are still a GIMPS participant!!!!
The Mersenne Newsletter, issue #15 April 3, 1999
Contents
1. Serious Bug Found in Version 17
2. EFF Announces $50,000 Prize For Finding Million Digit Prime!!!
3. Future Newsletters
4. Welcome New Members
5. PrimeNet Server News
6. ECM Factoring News
7. George's New Email Address
8. GIMPS Status Update
1. Serious Bug Found in Version 17
----------------------------------
Version 17 was released a few months ago to allow double-checking
previously tested exponents. Since about 1 in 100 previous tests are
incorrect, you can still find a Mersenne prime by double-checking.
This is the perfect chore for slower Pentiums. You don't have to wait
several months for each Lucas-Lehmer test to complete.
Unfortunately, a bug was introduced that affected tests on exponents
above 4,194,304. Download version 18 immediately at
http://www.mersenne.org/freesoft.htm or ftp://entropia.com/gimps
This bug affected about 11,000 out of 59,000 reported results above 4,194,304.
All results produced by version 16 are OK. All results that were started
by version 16 and completed by version 17 are OK. All factoring and
double-checking work is OK.
After upgrading to version 18, you may get error messages that look like this:
Error reading intermediate file: p6180331
Renaming intermediate file q6180331 to p6180331.
Error reading intermediate file: p6180331
This is normal. Prime95 must discard incorrect version 17 save files.
To those that have been using version 17 to test exponents above 4,194,304
I offer my sincerest apologies. I know that upgrading will be very
inconvenient and it will be disheartening to lose months of work. Sorry.
On the bright side, perhaps one of the 11,000 affected exponents will
turn out to be prime allowing someone to win a big prize described below!
2. EFF Announces $50,000 Prize For Finding Million Digit Prime!!!
-----------------------------------------------------------------
On March 31, the Electronic Frontier Foundation announced a $50,000
prize to be awarded to the first person to find a million digit
prime number! The details are available at http://www.eff.org/coop-awards/
Since GIMPS is now testing numbers well in excess of 1 million digits,
some lucky GIMPS member could very well win this prize!
If you are using business computers, a friend's computer, or a
co-worker's computer, I recommend you discuss how the $50,000 prize
would be divided should you be the lucky winner. Note that according
to the contest rules, you could be denied the prize if you have not
legally obtained permission to use the computer that finds the prime number.
In light of the EFF anouncement, the $1,500 prize fund for discovering
the 38th Mersenne prime has been discontinued.
3. Future Newsletters
---------------------
I will no longer email the Mersenne newsletter to every GIMPS user. Instead,
there will be three ways to get future newsletters:
1) Online at http://www.mersenne.org/prime.htm. Check periodically for
new editions.
2) Subscribe to the Mersenne mailing list. I will send future newsletters
to the mailing list.
3) Use the web form at http://entropia.com/ips/register.html to request
having future newsletters emailed to you. A link to the web form will
also be available from http://www.mersenne.org/prime.htm
4. Welcome
----------
Since the last newsletter 10 months ago, many thousands have joined GIMPS!
There are now 9,000 people and teams involved in the search. Welcome to all
the new searchers! I'm sorry your first newsletter had to announce bad
news. This is the first serious setback for GIMPS in its three and a half
year history.
5. PrimeNet Server news
-----------------------
Link your Top Producer's Page account name to your home page!
Check out the people, teams, businesses and schools behind the
top CPU time accounts at http://entropia.com/ips/tops.shtml,
and add your own page link!
If you are using the RPC protocol, please use the faster HTTP
protocol instead. You can select this option in the version 18
Windows software in the Test/PrimeNet dialog box. MPrime and
PrimeOS2 already use HTTP.
To get your full PrimeNet account report without a password
(for example, to use in a web page), email primenet@entropia.com
with your request to use this special account feature.
If PrimeNet emails you a confirmation that it received
a Mersenne prime from your computer, please remember worldwide
academic research discovery rules apply. Please contact me
immediately at woltman@alum.mit.edu, and do not communicate the
discovery until we have verified it on a conventional Cray
supercomputer. I will help you work with EFF to collect your
prize.
For other network, server or PrimeNet account related questions,
please email Scott Kurowski's team at primenet@entropia.com.
Entropia.com upgraded the GIMPS Internet PrimeNet Server on
9 February to PrimeNet 4.0, a powerful new system built on their
new v4 Internet computing technology. The 4.0 server offers
substantial reliability improvements and an order of magnitude
better performance and feature integration flexibility.
The thoughtful Entropia.com community of GIMPS participants
continues to grow. The PrimeNet virtual supercomputer is
currently producing about 550 billion floating point operations
per second, which puts it among the top 10 most powerful systems
in the world. This amazing strength arises from the spare CPU
time from your computer and some 15,500 others on 9,000
individual, team and business accounts. For more on
Entropia.com's PrimeNet system and related projects, see
http://entropia.com/ips and http://entropia.com, or email
info@entropia.com.
The GIMPS PrimeNet Server is provided by Entropia.com, Inc.
6. ECM factoring
----------------
The program now lets you find factors of small Mersenne numbers using the
Elliptic Curve Method. Mathematicians are interested in completely factoring
Mersenne numbers as well as finding new Mersenne primes. If this interests
you, visit http://www.mersenne.org/ecm.htm for more details. To date we have
discovered 16 new Cunningham factors, including Conrad Curry's largest factor
ever found using ECM.
7. New email address
--------------------
My new email address is woltman@alum.mit.edu. My old address,
woltman@magicnet.net, still works. In fact the new address simply forwards
mail to the magicnet address. However, should I ever change ISPs the new
address will forward my mail to the appropriate place.
8. Status
---------
In the ten months since the last newsletter GIMPS as accomplished
the following milestones:
* Double-checking proves M(1398269) is the 35th Mersenne prime.
* All exponents below M(2976221) tested at least once.
* All exponents below M(3021377) tested at least once.
* All Mersenne numbers less than a million digits tested at least once.
We have completed first-time Lucas-Lehmer tests on about 45,000 Mersenne
numbers. Of these 45,000 numbers tested, we expected to find one
Mersenne prime. We've been a bit unlucky.
However, there are still 396,543 exponents left to test below 20,500,000.
It will only take us 534,493 P-90 CPU years to test exponents and we expect
to find 3.71 Mersenne primes. At Primenet's current rate, we expect to
find one Mersenne Prime this year.
You can watch the hourly progress of the search on the server's
status page at http://entropia.com/primenet.
Conclusion
----------
Once again, I'm sorry about the version 17 bug. Best wishes and good luck
in the future. Hopefully someone will soon find the 38th Mersenne prime
and collect a nice prize! And I can write a more upbeat newsletter!
Sincerely,
George Woltman
woltman@alum.mit.edu
and
Scott Kurowski
primenet@entropia.com
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The Mersenne Newsletter, issue #16 July 6, 1999
Discovery of the 38th Mersenne Prime!!!
---------------------------------------
The Great Internet Mersenne Prime Search (GIMPS)
Finds First Million-Digit Prime,
Stakes Claim to $50,000 EFF Award.
2^6972593-1 is now the Largest Known Prime
Press release
http://www.mersenne.org/6972593.htm
GIMPS Home page and latest news links
http://www.mersenne.org/prime.htm
Congratulations to Nayan Hajratwala and all GIMPS members for
our fourth success! Good luck to all in the search for M39!
Sincerely,
George Woltman
woltman@alum.mit.edu
and
Scott Kurowski & team
primenet@entropia.com
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From woltman@alum.mit.edu Sun Oct 10 16:22:59 1999
To: <wedgingt@acm.org>
Subject: Mersenne Newsletter, issue #17
Date: 10 Oct 99 23:18:12 +-0100
To: Great Internet Mersenne Prime Search Registered Recipient
The Mersenne Newsletter, issue #17, October 10, 1999
Contents
1. New email address for George, mailto:woltman@alum.mit.edu
2. Faster version 19 now available
3. What's new in version 19?
4. Thanks
5. Note on estimated completion dates
6. GIMPS and the $100,000.00 EFF award
1. New email address
====================
My email address is woltman@alum.mit.edu. Please update your records.
My old magicnet email address will not work much longer.
2. Faster version 19 now available
==================================
Version 19 is now available and it is up to 10% faster!
Here are some sample per-iteration timings from my PII-400:
Exponent V18 timing V19 timing
3500000 0.104 0.0982 5.6% faster
4200000 0.1266 0.1193 5.8% faster
7000000 0.2292 0.2107 8.1% faster
8200000 0.278 0.2520 9.4% faster
You can get the new version at http://www.mersenne.org/freesoft.htm
To upgrade, stop and exit the current version. Optionally
make a backup of the directory. Unzip the new version on top of the
old version. Start the new version of the program.
Save files are upward compatible from previous versions but not
backward compatible. Thus, if you are in a dual-boot environment
make sure you upgrade the Windows and Linux versions at the same time.
3. What's new in version 19?
============================
1) Faster - in some cases as much as 10% faster!. The FFTs were recoded
for improved memory and TLB efficiency. Furthermore, optimizations
specific to the Pentium Pro and later processors were added.
2) New FFT lengths. The program can now test exponents as large as
79.3 million. Also, smaller FFT lengths are supported for use in
ECM and P-1 factoring.
3) More conservative FFT breakpoints. This could actually result in
a few exponents being slower to test in this version. However, the
chance of a fatal rounding error has been reduced.
4) P-1 factoring has been added. Although it is not very practical for
large exponents because of a slow GCD routine, it can be used to
find new factors of exponents below a few million or so.
5) ECM can now run on large exponents. Once again, the slow GCD routine
and high memory requirements might make this impractical for large
exponents.
6) ECM and P-1 factoring now support save files. Very handy on lengthy runs.
The count of completed ECM curves is maintained in the save file instead
of the worktodo.ini file.
7) ECM and P-1 factoring lets you specify the amount of memory to use.
In some cases, more memory can improve execution speed slightly.
8) A bug in guessing the CPU speed on initial install has been fixed.
9) The preferences dialog now has an option to pause prime95 when a laptop
is running on its battery.
10) Error checking has been improved slightly.
11) Factoring is now "layered". That is, prime95 now factors to 2^50, then
2^51, 2^52, and so forth up to the appropriate limit. The factoring
output lines have been changed to show percent complete in the current
"layer".
12) A bug in running two or more self or torture tests in the same directory
has been fixed.
13) Trial factoring above 2^64 is now supported.
14) More trial factoring is now done to take into account the cost of
double-checking.
15) Title now contains percent complete when LL testing. By default, the
percent complete value is now displayed to 2 decimal places. You can
change this by setting PercentPrecision in prime.ini to a value
between 0 and 6.
16) Affinity and service name settings moved from prime.ini to local.ini file.
Prime95 will automatically move these settings for you.
17) An option to get only 10,000,000 digit numbers to run primality tests
on has been added to the Test/Primenet dialog box. See
http://www.mersenne.org/prize.htm for rules on claiming the EFF award
for finding a 10,000,000 digit prime.
18) The Advanced/Clear primes menu choice has been deleted.
19) The prime95 icon turns yellow when the program is idle. After an
error such as ILLEGAL SUMOUT, the icon will blink for 10 seconds.
20) The User Information dialog box allows you to request newsletters and
form a team user ID where the team members cannot alter the team name.
21) A bug in the reporting of error counts in the results.txt file has
been fixed.
22) The server can now broadcast important messages to the prime95 client.
Prime95 will blink the icon until prime95 is activated and then it will
display the message.
23) A computer ID will be generated for computers that do not have one. If
you want to assign your own computer ID, please try to make each
computer ID using the same user ID unique.
4. Thanks
=========
I'd like to thank the excellent work of the QA team. They located
many bugs, bringing you a higher quality beta. The QA team included
Ken Kriesel, Brian Beesley, Tom Cage, Jean-Yves Canart, Bryan Fullerton,
Marc Getty, Steinar H. Gunderson, Eric Hahn, Alex Healy, Paul Landon,
Greg McIntyre, Lawrence Murray, Paul Victor Novarese, Ethan M. O'Connor,
Rick Pali, Shane Sanford, Brian Schroeder, Gordon Spence, Joth Tupper,
Guillermo Ballester Valor, David Willmore, and Lucas Wiman.
And, of course, thanks to Scott Kurowski's team at Entropia.com for the
v19 enhancements to the PrimeNet server and ongoing operational
support of GIMPS on the Entropia.com supercomputing network.
5. Note on estimated completion dates
=====================================
The timings in version 19 have been recalibrated to my PII-400 instead
of my old, deceased P-90.
What does that mean? The short explanation is that you should not
initially trust the estimates given in Test/Status. Over time these
estimates will become accurate again.
Why is this? When version 18 estimated my PII-400's speed it underestimated
by 40%. Over time, the RollingAverage value in local.ini grew to 1400
to compensate for the poor guess and give accurate estimates in Test/Status.
In version 19, the program accurately guesses my PII-400's speed and
applying the rolling average of 1400 makes it bring in the expected completion
dates by 40%. It won't take too long for the rolling average to come
down to close to 1000 -- or you can edit your local.ini file my hand and
set the RollingAverage to 1000. Also changing you CPU type in Test/CPU
will reset the RollingAverage to 1000.
6. GIMPS and the $100,000 EFF award
===================================
The Electronic Frontier Foundation is offering a $100,000 award to
the first group to find a ten million digit prime number. The details
of how GIMPS will handle this award is at http://www.mersenne.org/prize.htm
Fair warning: A 500 MHz PC will take a full year to test a single exponent
with only 1 chance in 250,000 of finding a prime number.
Sincerely,
George Woltman
woltman@alum.mit.edu
and
Scott Kurowski & Entropia.com, Inc.
primenet@entropia.com
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