1. Mersenne Prime Search An organized search for mersenne prime numbers. Free software provided. http://www.mersenne.org/prime.htm

GIMPS Home Page NEW: Mersenne Wiki Pages available in Chinese Danish Dutch German ... Italian , and Spanish . Warning: These translations may not be up-to-date - use AltaVista as necessary. Mersenne Wiki Created From the good folks that brought you the Mersenne Forums comes the Mersenne Wiki . Browse the Wiki to learn more about GIMPS and Mersenne Primes. If you're already knowledgeable, then consider contributing to the Wiki. 42nd Known Mersenne Prime Found! On February 18, 2005, Dr. Martin Nowak from Germany, found the new largest known prime number, 2 -1. The prime number has 7,816,230 digits ! It took more than 50 days of calculations on Dr. Nowak's 2.4 GHz Pentium 4 computer. The new prime was independently verified in 5 days by Tony Reix of Grenoble, France using a 16 Itanium CPU Bull NovaScale 5000 HPC running the Glucas program by Guillermo Ballester Valor of Granada, Spain. A second verification was completed by Jeff Gilchrist of Elytra Enterprises Inc. in Ottawa, Canada using 15 days of time on 12 CPUs of a Compaq Alpha GS160 1.2 GHz CPU server at SHARCNET Dr. Martin Nowak, an

2. Mersenne Prime Freeware Freeware to search for mersenne primes. Pointers to FreeLIP, GMP, HFloat, apfloat, CALC. http://www.samurai.com/mersenne/freeware.html

Mersenne Prime Freeware "Share and Enjoy" The Amdahl 6 's motto Mirror sites For increased performance, this page has been mirrored. Please choose the site closest to you for the best performance. www2.netdoor.com Conrad Curry, Southern US, master site www.samurai.com Bryan Fullerton, Canadian mirror Software Go to the GIMPS homepage . George Woltman's programs are the fastest on Intel chips running Windows 3.x, Windows 95/98/NT, OS/2, DOS, Linux and UNIXWARE. Software for Unix and non-X86 Check out Ernst Mayer's source code timings page for guidance as to which code is best for their platform. lucdwt.c on ftp.netdoor.com This is Dr. Richard Crandall's original Mersenne number testing program. Written in generic 'C'. George Woltman's lightening fast Pentium program has its roots in this code. Reported to be OK Sun Ultra Enterprise 3000 with Solaris 2.5.1 Linux (i386) other UNIX flavors mers on www.garlic.com mers 6.50 README HTML file about mers package mers.tar.gz binary 'tar xzf mers.tar' (FSF/GNU tar) or 'gunzip mers.tar; tar xf mers.tar' Windows users: WinZIP can read this file. Rename it to 'mers.tgz'.

3. The Mersenne Prime Homepage Notes and links by Simon RubinsteinSalzedo. http://www.albanyconsort.com/mersenne/

MERSENNE PRMES Nayan Hajratwala, George Woltman , Scott Kurowski, et. al. found the largest Mersenne Prime ever! It is 2^6972593-1. It is believed to be the 38th Mersenne Prime. It was found by a program by the Great Internet Mersenne Prime Search My club, GIMPS , has the program, called Prime, or Prime 95, by George Woltman Visit the mailing list of Mersenne Primes . P. S. If you don't want a lot of e-mail DON'T click here. Yes. I'm a member of that, too. CELEBRATE MERSENNE DAY EVERY DECEMBER 7TH! Mersenne Pages Mersenne Mailing list Luke's Marin Mersenne Page http://users.delta.com/mersenne/prime.txt The Largest Known Prime by Year: A Brief History ... My homepage

4. Mersenne Prime Digits Landon Curt Noll lists the decimal, English, and American expansions of all theknown mersenne primes. http://www.isthe.com/chongo/tech/math/prime/mersenne.html

Mersenne Prime Digits and Names Prime number pages English Name of a Number Mathematics / Cryptology / Cryptography pages Technology pages ... chongo's home page Known Mersenne Primes 1000 digit primes 10,000 digit primes 100,000 digit primes 1,000,000 digit primes ... Some useful links Mersenne Prime Discovery Date Digit Count Decimal Digits English Name English Name with -'s American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style Mersenne Prime Discovery Date Digit Count Decimal Digits English Name English Name with -'s American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style Mersenne Prime Discovery Date Digit Count Decimal Digits English Name English Name with -'s American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style European style American style

5. Mersenne Prime Mailing List Unmoderated list for communication between those interested in all aspects of mersenne primes. Sginup and access to archives. http://www.ndatech.com/mersenne/signup.htm

Mersenne Prime Mailing List Sign-Up Sheet The Mersenne Prime Mailing List was created to facilitate communication between those interested in all aspects of Mersenne Primes. One ongoing topic is the search for the next Mersenne Prime. The list is unmoderated. You can read all of the old posts in the list's older archives . You can also find some of the list's older digest archives and a recent searchable achive You are encouraged to read the FAQ before posting. This list is made possible by web pioneer Gordon Irlam who has generously configured his machine, base.com , to host the list. Thank you, gordoni! It is important to understand that there are THREE email addresses: the list itself is mersenne @base.com, send messages to everybody list maintenance is mersenne- request @base.com, ask to get on or off the list list maintenance is mersenne-digest- request @base.com, ask to get on or off the magazine version If you are having problems, there is a fourth address where you can ask the people running the list for help. Send email to: Me: marin@ndatech.com

6. Mersenne Primes History, Theorems And Lists See also Where is the next larger mersenne prime? and Mersenne heuristics. For remote pages on Mersennes see the Prime Links' Mersenne directory http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. Free Software Free software to find new mersenne prime numbers. has a web page that pointsto available source code you can use to help search for mersenne primes. http://www.mersenne.org/freesoft.htm

Download February 2005: New Mersenne Prime!! Free - you can't beat that price! You need a Pentium-class computer with Windows, OS/2, Linux, or FreeBSD. You must also agree to abide by the prize distribution rules . PowerPC owners can also participate. Unix and non-x86 users should check out Ernst Mayer's Mlucas page and the Glucas page for guidance as to which code is best for their platform. The How it works and FAQ pages answer many questions you may have before downloading the software. In case of downloading difficulties, a Russian mirror site is available. Version 24 released! Upgrade instructions This version contains many performance improvements for Athlon and Pentium 4 users. See whatsnew.txt for the full list of improvements. Step 1. You can upgrade even if you are in the middle of testing an exponent. Stop and exit the current version of the program. Optionally back up the directory. Step 2. Download the appropriate program for your OS. Step 3. Install the new version overwriting the previous version Step 4.

8. The Largest Known Primes The largest known prime has almost always been a mersenne prime. Why Mersennes? Because the way the largest numbers N are proven prime is based http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. Mersenne Prime -- From MathWorld A mersenne prime is a Mersenne number, ie, a number of the form Note thatthe region after the 38th known mersenne prime has not been completely http://mathworld.wolfram.com/MersennePrime.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Special Numbers Prime-Related Numbers ... Mathematical Records Mersenne Prime A Mersenne prime is a Mersenne number , i.e., a number of the form that is prime . In order for to be prime must itself be prime . This is true since for composite with factors and . Therefore, can be written as , which is a binomial number that always has a factor The first few Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... (Sloane's ) corresponding to indices , 3, 5, 7, 13, 17, 19, 31, 61, 89, ... (Sloane's Mersenne primes were first studied because of the remarkable properties that every Mersenne prime corresponds to exactly one perfect number . L. Welsh maintains an extensive bibliography and history of Mersenne numbers. It has been conjectured that there exist an infinite number of Mersenne primes. Fitting a line fixed to pass through the origin to the asymptotic number of Mersenne primes with gives a best-fit line with . If the line is not restricted to pass through the origin, the best fit is

10. Mersenne Prime Search An organized search for mersenne prime numbers. Free software provided. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. MathWorld News: 42nd Mersenne Prime (Probably) Discovered February 18, 2005Less than a year after the 41st mersenne prime was reported If verified, this would be the 42nd known mersenne prime, as well as the http://mathworld.wolfram.com/news/2005-02-18/mersenne/

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon MathWorld Headline News 42nd Mersenne Prime (Probably) Discovered By Eric W. Weisstein February 18, 2005Less than a year after the 41st Mersenne prime was reported ( MathWorld headline news: June 1, 2004 ), Great Internet Mersenne Prime Search (GIMPS) project organizer George Woltman is reporting in a Feb. 18 email to the GIMPS mailing list that a new Mersenne number has been flagged as prime and reported to the project's server. If verified, this would be the known Mersenne prime, as well as the largest prime number known of any kind. Addendum : As of February 25, the new Mersenne prime has been verified, as communicated by Woltman in a Feb. 25 email. More details will be provided as they become available.] Mersenne numbers are numbers of the form M n n - 1, giving the first few as 1, 3, 7, 15, 31, 63, 127, .... Interestingly, the definition of these numbers therefore means that the

12. Mersenne Prime Search Online search for mersenne prime numbers, found largest several primes. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Mersenne Primes: History, Theorems And Lists The definitive pages on the mersenne primes and the related mathematics! http://primes.utm.edu/mersenne/

Mersenne Primes: History, Theorems and Lists A forty second Mersenne found Feb 2005: Contents: Early History Perfect Numbers and a Few Theorems Table of Known Mersenne Primes The Lucas-Lehmer Test and Recent History ... Conjectures and Unsolved Problems See also Where is the next larger Mersenne prime? and Mersenne heuristics For remote pages on Mersennes see the Prime Links' Mersenne directory Primes: Home Largest Proving How Many? ... Mailing List 1. Early History Many early writers felt that the numbers of the form 2 n -1 were prime for all primes n , but in 1536 Hudalricus Regius showed that 2 -1 = 2047 was not prime (it is 23 89). By 1603 Pietro Cataldi had correctly verified that 2 -1 and 2 -1 were both prime, but then incorrectly stated 2 n -1 was also prime for 23, 29, 31 and 37. In 1640 Fermat showed Cataldi was wrong about 23 and 37; then Euler in 1738 showed Cataldi was also wrong about 29. Sometime later Euler showed Cataldi's assertion about 31 was correct. Enter French monk Marin Mersenne (1588-1648). Mersenne stated in the preface to his

14. Ars Technica Team Prime Rib Information, stats, FAQ, and chat room on how they support the mersenne prime Search. http://www.teamprimerib.com/rr1/

TEAM PRIME RIB Home Chat Room guide TPR Seventeen or Bust TPR Number Field Sieve Top Teams Pages Top Producers Report Top Producer Graphs Top Factoring Report Top Factoring Graphs ... Team Overtake Report Assigned Exponents Team Summary Team Graphs Member Summary Double Checking ... The Orphanage Cleared Exponents Recent Summary Member Summary Member Output Member Graphs ... Incorrect Team Results Links P90 CPU yrs Calculator Gimps Home Page Gimps Forum PrimeNet Home ... Ars Technica Team Summary Run Date : 16-Sep-2005 23:50 UTC (Sep 16 2005 19:50 EDT) Last Primenet Report Date : 16-Sep-2005 22:58 UTC Team Exponent Health Recently Assigned or Checked in Not checked in Recently Overdue/Near Expiry Lucas-Lehmer Double Checking Trial Factoring Totals Number Of Exponents Assigned Number Of Members Number Of Computers Assigned Total Ghz Assigned * Totals may not tally due to computers with more than one type of exponent assigned Computers Added Recently Computer Id Mhz Ver Member Date Added endlesmike 16-Sep-05 DSheets 16-Sep-05 DSheets 16-Sep-05 DSheets 16-Sep-05 DSheets 16-Sep-05 16-Sep-05 16-Sep-05 16-Sep-05 16-Sep-05 16-Sep-05 16-Sep-05 16-Sep-05 16-Sep-05 Exponents due to expire within 14 days Exponent Type Bits Iteration Days Date Computer Id Member Run Expiry Updated Assigned L 17-Jul-05 Annie Annie L 19-Jul-05 Annie Annie L 05-Jul-05 22-Jun-05 lowcrawler L 23-Jun-05 sakarov sakarov L 21-Jul-05 Annie Annie L 21-Jul-05 21-Jul-05 Annie Annie L 21-Jul-05 19-Jul-05 Annie Annie L 21-Jul-05 11-Jul-05 DSheets L 21-Jul-05 01-May-05 DSheets L 15-Jul-05 22-Jun-05 Rarian L 16-Jul-05 11-Jul-05 Rarian L 22-Jul-05 Annie Annie L 22-Jul-05

15. Mersenne Prime Numbers mersenne prime Numbers http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

16. The Largest Known Primes The Great Internet mersenne prime Search (GIMPS) was launched by George mersenne primes are primes of the form 2p1. These are the easiest type of http://primes.utm.edu/largest.html

The Largest Known PrimesA Summary (An historic Prime Page resource since 1994!) Last modified: 23:20:23 Friday September 16 2005 UTC News note: GIMPS found: 2 -1, the 42nd known Mersenne! Announced February 26, 2005. Contents: Introduction (What are primes? Who cares?) The Top Ten Record Primes largest twin ... Mersenne , and Sophie Germain The Complete List of the Largest Known Primes Other Sources of Prime Information Euclid's Proof of the Infinitude of Primes Primes: Home Largest Proving How Many? ... Mailing List Note: The correct URL for this page is http://primes.utm.edu/largest.html This page summarizes the information on the list of 5000 Largest Known Primes 1. Introduction An integer greater than one is called a prime number if its only positive divisors (factors) are one and itself. For example, the prime divisors of 10 are 2 and 5; and the first six primes are 2, 3, 5, 7, 11 and 13. ( The first 10,000 , and other lists are available). The Fundamental Theorem of Arithmetic shows that the primes are the building blocks of the positive integers: every positive integer is a product of prime numbers in one and only one way, except for the order of the factors. (This is the key to their importance: the prime factors of an integer determines its properties.) The ancient Greeks proved (ca 300 BC) that there were infinitely many primes and that they were irregularly spaced (there can be arbitrarily large gaps between successive primes ). On the other hand, in the nineteenth century it was shown that the number of primes less than or equal to

17. Perfectly Scientific - Home New poster! New largest prime number! The prime is 2259649511, discovered in February 2005. Algorithm contracting http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

18. Mersenne Prime Search Online search for mersenne prime numbers, found largest several primes. http://www.mersenne.org/

GIMPS Home Page NEW: Mersenne Wiki Pages available in Chinese Danish Dutch German ... Italian , and Spanish . Warning: These translations may not be up-to-date - use AltaVista as necessary. Mersenne Wiki Created From the good folks that brought you the Mersenne Forums comes the Mersenne Wiki . Browse the Wiki to learn more about GIMPS and Mersenne Primes. If you're already knowledgeable, then consider contributing to the Wiki. 42nd Known Mersenne Prime Found! On February 18, 2005, Dr. Martin Nowak from Germany, found the new largest known prime number, 2 -1. The prime number has 7,816,230 digits ! It took more than 50 days of calculations on Dr. Nowak's 2.4 GHz Pentium 4 computer. The new prime was independently verified in 5 days by Tony Reix of Grenoble, France using a 16 Itanium CPU Bull NovaScale 5000 HPC running the Glucas program by Guillermo Ballester Valor of Granada, Spain. A second verification was completed by Jeff Gilchrist of Elytra Enterprises Inc. in Ottawa, Canada using 15 days of time on 12 CPUs of a Compaq Alpha GS160 1.2 GHz CPU server at SHARCNET Dr. Martin Nowak, an

19. Mersenneforum.org A forum about prime numbers and computerized searches for more of them. Includes discussions of software and hardware issues encountered by http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

20. Landon Curt Noll's Prime Pages Slowinski and Gage s discovery of the 34th mersenne prime. Slowinski and Gage slarge mersenne prime is 212577871 (see also M1257787) http://www.isthe.com/chongo/tech/math/prime/

Prime numbers, Mersenne Primes, Perfect Numbers, etc. Mersenne Prime Digits and Names English Name of a Number Mathematics / Cryptology / Cryptography pages Technology pages ... chongo's home page Known Mersenne primes: of known Mersenne primes The largest known prime The 25th Mersenne prime is (see also M The 25th Perfect number is The 26th Mersenne prime is (see also M The 26th Perfect number is As a member of the Amdahl 6, I Co-Discovered these primes: The Amdahl 6 group The largest Amdahl 6 prime: The 3rd largest Amdahl 6 twin prime: The 2nd largest Amdahl 6 twin prime: The largest Amdahl 6 twin prime: The Amdahl 6 method for finding large non-Mersenne primes I am a member of the EFF Cooperative Computing Awards Team: EFF Cooperative Computing Awards home page EFF Cooperative Computing Awards official rules EFF Cooperative Computing Awards FAQ EFF Prime Number Resources and Info Slowinski and Gage's discovery of the 34th Mersenne prime: Slowinski and Gage's large Mersenne prime is (see also M Slowinski and Gage's large Perfect number is A San Jose Mercury News article about Slowinski and Gage's discovery My Press release about Slowinski and Gage's discovery Misc prime numbers: In private correspondence with Chris K. Caldwell

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