1. Mersenne Prime Search 41st Known mersenne prime Reported!! On May 15, 2004, a GIMPS computer reportedfinding the 41st known mersenne prime. 40th Known mersenne prime Found!! http://www.mersenne.org/prime.htm

GIMPS Home Page New Mersenne Prime Found!!! Pages available in Chinese Danish Dutch French ... Italian , and Spanish . Warning: These translations may not be up-to-date - use AltaVista as necessary. 41st Known Mersenne Prime Found!! On May 15, 2004, Josh Findley discovered the 41st known Mersenne Prime, 2 -1. The number is nearly a million digits larger than our last find and is now the largest known prime number! Congratulations to Josh and every GIMPS contributor for their part in this remarkable find. You can download the client for your chance at finding the next world record prime! A forum for newcomers is available to answer any questions you may have. Josh's calculation took just over two weeks on his 2.4 GHz Pentium 4 computer. Josh has been a GIMPS participant for 5 years, proving the value of having great patience. The new prime was verified by Tony Reix in just 5 days using only half the power of a Bull NovaScale 5000 HPC running Linux on 16 Itanium II 1.3 GHz CPUs. A second verification was completed by Jeff Gilchrist of Elytra Enterprises Inc. in Ottawa, Canada using eleven days of time on a HP rx5670 quad Itanium II 1.5 GHz CPU server at

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. Mersenne Prime Digits mersenne prime Digits and Names Largest known prime) (Some useful links) Mersenne. Prime. Discovery. Date. Digit 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 Single line American style European style American style European style American style European style Single line American style European style American style European style American style European style Single line American style European style American style European style American style European style Single line 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 Single line American style European style American style European style American style European style Single line American style European style American style European style American style European style Single line American style European style American style European style American style European style Single line 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 Single line American style European style American style European style American style European style Single line American style European style American style European style American style European style Single line

4. Free Software What to do if you re running UNIX? Luke Welsh has a web page that points toavailable source code you can use to help search for mersenne primes. http://www.mersenne.org/freesoft.htm

Download New Mersenne Prime Found!!! Free - you can't beat that price! You need a Pentium-class computer with Windows 3.1, Windows 95/98/Me, Windows NT/2000/XP, 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 source code timings 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, European and Russian mirror sites are available. Version 23 released! Upgrade instructions This version contains many performance improvements for Pentium 4 users. It is up to 25% faster than version 22. Athlon and Pentium 3 users will see a small speed increase too. The Windows version also has small improvements in the torture test. 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.

5. Mersenne Primes: History, Theorems And Lists The definitive pages on the mersenne primes and the related mathematics! See also Where is the next larger mersenne prime? and Mersenne heuristics. For remote pages on Mersennes each case 2n1 was a mersenne prime? In fact it is http://www.utm.edu/research/primes/mersenne.shtml

Mersenne Primes: History, Theorems and Lists A forty first Mersenne found May 2004: 2 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 Cogitata Physica-Mathematica (1644) that the numbers 2 n -1 were prime for n 31, 67, 127 and 257

6. 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

7. BBC News | SCI/TECH | Number Takes Prime Position The largest prime number yet discovered is revealed to the world all four million digits. by 2 and 5 A mersenne prime is a prime of the form 2P-1 The first Mersenne 7, 11. A mersenne prime http://news.bbc.co.uk/hi/english/sci/tech/newsid_1693000/1693364.stm

CATEGORIES TV RADIO COMMUNICATE ... INDEX SEARCH You are in: Sci/Tech Front Page World UK ... AudioVideo SERVICES Daily E-mail News Ticker Mobiles/PDAs Feedback ... Low Graphics Wednesday, 5 December, 2001, 11:42 GMT Number takes prime position By BBC News Online science editor Dr David Whitehouse The largest prime number yet discovered has just been revealed to the world. There are more primes out there George Woltman, Gimps founder The new number, expressed as 2 -1, contains 4,053,946 digits and would take the best part of three weeks to write out longhand. The prime number - a number that can only be divided by one and itself - was discovered by Michael Cameron, a 20-year-old Canadian participant in a mass computer project known as the Great Internet Mersenne Prime Search (Gimps). Mersenne primes are important for the theory of numbers and they may help in developing unbreakable codes and message encryptions. The Gimps project spent 13,000 years of computer time to find the new prime number. Big effort Cameron used an 800 MHz AMD T-Bird PC, running part-time for 45 days to find the number.

8. Mersenne Prime Numbers mersenne primes. Marin Mersenne ( 15881648) was a Franciscan friar who lived most of his life in Parisian cloisters. He was the author of Cognitata Physico-Mathematica which stated without proof that Mp is prime for p = The concept of a mersenne prime is evolved from that of a perfect number A mersenne prime is such a number Mp, where p is prime http://www.resort.com/~banshee/Info/mersenne.html

Mersenne Primes Marin Mersenne (1588-1648) was a Franciscan friar who lived most of his life in Parisian cloisters. He was the author of Cognitata Physico-Mathematica which stated without proof that M p is prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, and 257 and for no other primes p for p < 257. It took over 300 years to totally settle this claim made by Mersenne. The final work done in 1947 showed that Mersenne made five errors in his work (namely that M is prime, M is composite, M is prime, M is prime, and M is composite). Besides his famous statement about primes of the form M p , Mersenne contributed to the development of number theory through his extensive correspondence with many mathematicians, including Fermat. Mersenne effectively served as a clearing house and a disseminator of new mathematical ideas in the 17th century. Kenneth Rosen, Elementary Number Theory; Addison Wesley The concept of a Mersenne Prime is evolved from that of a perfect number . A perfect number is an integer for which the sum of its divisors is twice the number. For example: (6) = 1 + 2 + 3 + 6 = 12 = 2*6 thus 6 is a perfect number.

9. The Great Internet Mersenne Prime Search (GIMPS) The Great Internet mersenne prime Search (GIMPS) This Internet site provides news and information relating to the Great Internet mersenne prime Search's (GIMPS) mission to find worldrecord prime http://rdre1.inktomi.com/click?u=http://www.mersenne.org/prime.htm&y=02D7A8B

10. Mersenne Primes: History, Theorems And Lists numbers. Definition When 2 n 1 is prime it is said to be a mersenne prime.It respectively)? And that in each case 2 n -1 was a mersenne prime? In http://www.utm.edu/research/primes/mersenne/

Mersenne Primes: History, Theorems and Lists A forty first Mersenne found May 2004: 2 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 Cogitata Physica-Mathematica (1644) that the numbers 2 n -1 were prime for n 31, 67, 127 and 257

11. The Largest Known Primes a student in Ontario, is one of about 120,000 individuals involved in GIMPS theGreat Internet mersenne prime Search launched by Woltman in early 1996. http://www.utm.edu/research/primes/largest.html

The Largest Known Primes (A historic Prime Page resource since 1994!) News note: New GIMPS find: 2 -1, the 41st known Mersenne! Announced May 28, 2004. 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 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

12. Mersenne Prime From MathWorld mersenne prime from MathWorld A Mersenne number which is prime is called a mersenne prime. In order for the Mersenne number M_n, defined by M_n\equiv 2^n1, to be prime, n must itself be prime http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/MersennePrime.html

13. Mersenne Prime -- From MathWorld mersenne prime. A Mersenne number which is prime is called a Mersenneprime. Every mersenne prime gives rise to a perfect number. http://mathworld.wolfram.com/MersennePrime.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Number Theory Numbers Large Numbers ... Prime-Related Numbers 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 n must itself be prime . This is true since for composite n with factors r and s n = rs . Therefore, can be written as which is a binomial number and can be factored. The first few Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... (Sloane's ) corresponding to n = 2, 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, although finding them is computationally very challenging. For example, the discovery that

14. MathWorld News: 40th Mersenne Prime Announced 40th mersenne prime Announced. By Eric W. Weisstein with contributions by Ed Pegg,Jr. GIMPS The Great Internet mersenne prime Search. www.mersenne.org. GIMPS. http://mathworld.wolfram.com/news/2003-12-02/mersenne/

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon MathWorld Headline News 40th Mersenne Prime Announced By Eric W. Weisstein with contributions by Ed Pegg, Jr. December 2, 2003Almost exactly two years after the 39th largest Mersenne prime was discovered ( MathWorld headline news: November 14, 2001 , announcement; December 5, 2001 , confirmation), 2 - 1, a number having 6,320,430 decimal digits, has been identified as a Mersenne prime, making it the largest such number as well as, by far, the largest known prime discovered to date. This news followed a November 17 report ( MathWorld headline news: November 19, 2003 ) on the Great Internet Mersenne Prime Search (GIMPS) website announcing that a new Mersenne number passed the Lucas-Lehmer test , thus identifying it as a prime number. Mersenne numbers are numbers of the form M n n - 1. For example

15. SS > Factoids > Mersenne Prime home factoids mersenne prime. mersenne prime. A prime number of the form where p is prime The GREAT Internet mersenne prime Search help find another mersenne prime http://public.logica.com/~stepneys/cyc/m/mersenne.htm

home factoids Mersenne prime A prime number of the form where p is prime. The Mersenne number Mp is prime for exponent p For all other prime exponents less than Mp is composite, and for those less than 12,441,900 it is probably composite. ... it is the greatest that will ever be discovered for, as they are merely curious without being useful, it is not likely that any person will attempt to find one beyond it. Peter Barlow 1811, on M Mersenne numbers have a particulary simple test for primality, the Lucas-Lehmer test The number-theoretic interest in Mersenne primes comes from the following theorem: if m and n are natural numbers, with n greater than 1, and if m n -1 is prime, then m is 2 and n is prime. Each Mersenne prime corresponds to an even perfect number The GREAT Internet Mersenne Prime Search help find another Mersenne prime! Chris Caldwell's Mersenne Primes Page history, lists, theorems, conjectures, ... Luke Welsh's Marin Mersenne Page biographies, prime number lists, algorithms, bibliography, ...

16. Landon Curt Noll's Prime Pages Slowinski and Gage s discovery of the 34th mersenne prime Known mersenne primeDigits and Names; Caldwell s article on the discovery of 2 13466917 1; 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

17. Frequently Asked Questions About the mersenne prime Freeware. http://www.mersenne.org/faq.htm

Frequently Asked Questions New Mersenne Prime Found!!! This FAQ is out-of-date and updated infrequently. The GIMPS forums provide may provide a better way for you to search for answers or ask new questions and get answers from long-time GIMPS members. This page contains answers to some of the frequently asked questions about the Mersenne Prime Freeware. It answers questions about what the program does and how to use it. It does not answer questions about networking problems or questions about the PrimeNet server. For answer's to those questions visit the PrimeNet server's FAQ General Questions Will the program interfere with my normal work? Will my computer have to be on all the time? What if my computer crashes? Will running my computer 24 hours a day shorten its lifespan? What are Mersenne primes? How are they useful? ... Can I participate if my computer doesn't have an Internet connection? Using the Program What does the screen output mean? What is the difference between factoring, double-checking, and Lucas-Lehmer testing? Why does this utility I have say the program is running at normal priority? Will the program run faster if I raise the priority? ... I own a dual-CPU computer or several computers networked together. Can these CPUs work together on the same exponent to get results faster? Will the program interfere with my normal work? Highly unlikely. The program runs at the lowest possible priority. This means it runs only when you are not using your computer for other purposes. However, the program will use about 8MB of memory. If your computer is low on memory, running the program could increase thrashing and cause other programs to run a bit slower. For more information, see the

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

GIMPS Home Page New Mersenne Prime Found!!! Pages available in Chinese Danish Dutch French ... Italian , and Spanish . Warning: These translations may not be up-to-date - use AltaVista as necessary. 41st Known Mersenne Prime Found!! On May 15, 2004, Josh Findley discovered the 41st known Mersenne Prime, 2 -1. The number is nearly a million digits larger than our last find and is now the largest known prime number! Congratulations to Josh and every GIMPS contributor for their part in this remarkable find. You can download the client for your chance at finding the next world record prime! A forum for newcomers is available to answer any questions you may have. Josh's calculation took just over two weeks on his 2.4 GHz Pentium 4 computer. Josh has been a GIMPS participant for 5 years, proving the value of having great patience. The new prime was verified by Tony Reix in just 5 days using only half the power of a Bull NovaScale 5000 HPC running Linux on 16 Itanium II 1.3 GHz CPUs. A second verification was completed by Jeff Gilchrist of Elytra Enterprises Inc. in Ottawa, Canada using eleven days of time on a HP rx5670 quad Itanium II 1.5 GHz CPU server at

19. The Mersenne Prime Homepage Nayan Hajratwala, George Woltman, Scott Kurowski, et. al. found the largest MersennePrime ever! It is . It is believed to be the 38th mersenne prime. http://www.albanyconsort.com/mersenne/mersenne.html

Mersenne Primes Nayan Hajratwala, George Woltman , Scott Kurowski, et. al. found the largest Mersenne Prime ever! It is . 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. From one year to the next, the largest prime number is usually a Mersenne prime, because they are much easier to check. Mersenne primes, and Mersenne numbers in general, were discovered by the French monk Marin Mersenne, who is depicted in the picture above. There are two main ways to find these numbers: one is to use a supercomputer, such as a Cray T3E. The other way is get a lot of personal computers together. This is what George Woltman did. There are now over 6000 participants in George's Mersenne club. David Slowinsky might never find another Mersenne prime. George's club has found the last four: , and and has also completed various other search goals, such as proving that M32, 33, 34, and 35 are the numbers we originally expected that they were, by testing all the ones in between.

20. Will Edgington's Mersenne Page Quick links to other Mersenne and Prime number related sites. The known factorsof M(p) 2, where M(p) is a mersenne prime, are in M3status.txt . http://www.garlic.com/~wedgingt/mersenne.html

Quick links to other Mersenne related files on my site update.txt : Date of last update of the data files. M3status.txt : Data about factorization of M(p) - 2 for prime M(p). MMPstats.txt : Data about factorization of M(M(p)) for prime M(p). facntD.txt : Factor counts for completely factored M(n) for all n > 1. facntHU.txt : Factor counts for incompletely factored M(n), n > 1. facpriks.gz : All known factors for M(p) for primes p, M(p) not factored. factoredM.txt : All known factors for M(n) for all M(n) completely factored. mersdata.zip : lowM.txt, DATABASE, DB.nf, primeM.txt, factoredM.txt, etc., zipped mersfmt.txt : Description of data format used in lowM.txt, factoredM.txt, etc. newsletters.html : All of George Woltman's GIMPS newsletters. primeM.txt : List of primes p for which M(p) is known to be prime. querylang.txt : Old draft of Mersenne data query language. Quick links to other Mersenne and Prime number related sites Mersenne Prime Project (George Woltman) Links to other math projects Chris Caldwell's Prime numbers pages Chris Caldwell's Mersenne pages ... Fermat number factoring status (Jocelyn Larouche) Mersenne Numbers "Mersenne numbers" are, by definition, numbers of the form:

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