21. Prime Info Page This list is for discussions relating to the Great Internet mersenne prime Search (gimps, http//www.mersenne.org), mersenne primes, Lucas Lehmer http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

22. Mersenne Prime - Wikipedia, The Free Encyclopedia mersenne primes have a close connection to perfect numbers, Historically,the study of mersenne primes was motivated by this connection; http://en.wikipedia.org/wiki/Mersenne_prime

Mersenne prime From Wikipedia, the free encyclopedia. In mathematics , a Mersenne prime is a prime number that is one less than a power of two . For example, 3 = 4 − 1 = 2 − 1 is a Mersenne prime; so is 7 = 8 − 1 = 2 − 1. On the other hand, 15 = 16 − 1 = 2 − 1, for example, is not a prime, because 15 is divisible by 3 and 5. More generally, Mersenne numbers (not necessarily primes, but candidates for primes) are numbers that are one less than a power of two; hence, M n n Mersenne primes have a close connection to perfect numbers , which are numbers that are equal to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC Euclid demonstrated that if M is a Mersenne prime then M(M+1)/2 is a perfect number. Two millennia later, in the 18th century Euler proved that all even perfect numbers have this form. No odd perfect numbers are known, and it is suspected that none exists. It is currently unknown whether there is an infinite number of Mersenne primes Contents Properties of Mersenne numbers Searching for Mersenne primes List of Mersenne primes See also ... edit Properties of Mersenne numbers Mersenne numbers share several properties: M n is a sum of binomial coefficients: If a is a divisor of M q (q prime) then a and: A theorem from Euler about numbers of the form shows that M q (q prime) is a prime if and only if there exists only one pair x y such that: M q x y with . More recently, Bas Jansen has studied

23. 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 This FAQ is out-of-date and updated infrequently.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

24. Mersenne Prime Mailing List Subscribe (or unsubscribe) to the mersenne prime Mailing List. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

25. Talk:Mersenne Prime - Wikipedia, The Free Encyclopedia I m no mathematician, but shouldn t the definition of mersenne prime include Obviously to be a candidate for a mersenne prime a number must be one less http://en.wikipedia.org/wiki/Talk:Mersenne_prime

Talk:Mersenne prime From Wikipedia, the free encyclopedia. I'm no mathematician, but shouldn't the definition of Mersenne prime include that it has to be one less than an natural power of two? Also, in the chart of Mersenne primes, shouln't the first entry be 2^0 - 1, which is 0? It is easy to see that 2 p -1 is prime iff p is prime... I'm not sure its really easy at all... maybe I'll wait for the proof to come up on the Prime numberss page; but in the mean time, the sentence should be reworded for a regular guy (like me) to know whats going on. cM It is not hard. If p is not prime, then you can write p as qr. It is easy to see that 2^q-1 and 2^r-1 are then divisors of 2^p-1 and therefore 2^p-1 is not prime either. The reason is obvious if you write 2^p-1 in the binary form. It looks like the digit "1" repeated p times (1111...). Similarly, 2^q-1 is the number 1 repeated q times. For example, 2^15-1 is 111111111111111, and 2^3-1 is 111, and the latter is obviously a divisor of the former because the ratio is 1001001001001. See also my text at the bottom. Lumidek 14:04, 6 Jun 2004 (UTC)

26. Ars Technica Team Prime Rib A distributed computing team dedicated to finding mersenne prime numbers. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

27. Will Edgington's Mersenne Page Downloadable factor data, newsletter archives, and proofs of theorems relatingto the search for mersenne primes. 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). Mersenneplustwo : Other web site with data about factors of M(p) + 2. 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.txt : List of files with all known factors for M(p) for primes p, M(p) not factored. results.pfk.split.aa.gz : First file listed in facpriks.txt. Links to rest of the pieces. 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:

28. Ars Technica Team Prime Rib A distributed computing team dedicated to finding mersenne prime numbers. http://www.teamprimerib.com/

29. SS > Factoids > Mersenne Prime Each mersenne prime corresponds to an even perfect number. The GREAT Internetmersenne prime Search help find another mersenne prime! http://www-users.cs.york.ac.uk/~susan/cyc/m/mersenne.htm

home factoids Mersenne prime A prime number of the form where p is prime. The Mersenne number M p is prime for exponent p For all other prime exponents less than M p is composite, and for those less than 15,130,000 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, ...

30. Internet PrimeNet Server PrimeNet is a distributed computing project for the Great Internet mersenne prime Search, coordinating the assignment of work and collection of results. http://www.mersenne.org/ips/

2^p-1 Internet PrimeNet Server Parallel Technology for the Great Internet Mersenne Prime Search PrimeNet World Test Status Updated Hourly PrimeNet Individual Account Reports PrimeNet Top Producers Awards Updated Hourly PrimeNet News and Information PrimeNet Statistics Charts PrimeNet Frequently Asked Questions GIMPS Home Serious research. Totally for fun. Join a search of mathematical discovery and become a part of Internet history. USD $100,000.00 Research Discovery Contest Free Participation Software Software for your Computer Proxy Service Software for LAN Gateways How to Get Peak Performance News, Information GIMPS PrimeNet News Newsletter Registration About PrimeNet PrimeNet Project Credits v22.12 Mersenne Research Software Released 8 November 2002 - GIMPS distributes v22.12 update of Prime95

31. Mersenne Primes: History, Theorems And Lists A comprehensive summary of mersenne prime matters, from their earliest history to the modern test implementations by computer. http://www.utm.edu/research/primes/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

32. GIMPS MERSENNE PRIME WORLD RECORD LARGEST FOUND BY GORDON SPENCE On Sunday 24th August 1997 I found the 36th mersenne prime at the time it was Stands for the Great Internet mersenne prime Search, and is a world wide http://www.rugeley.demon.co.uk/gimps/prime.htm

Great Internet Mersenne Prime Search and I found it !! Links Go Key Resource Number Theory Topic 36th Mersenne Prime Found On Sunday 24 th August 1997 I found the 36 th Mersenne Prime at the time it was the world's largest known prime number. It took my Pentium 100 PC fifteen days to prove the number prime. David Slowinski has verified the result on a Cray T90 Supercomputer. This new number is digits in length. George Woltman's announcement Chris Caldwell's announcement Read about it in Science News Article in the London Times ... CNN Article How big is that ? It would fill a 450 page paperback book If written out it would stretch for 1.4 miles or 2.2 Km It would take 28 days to say the number, speaking for 8 hours a day Please note though that I was just the lucky one of over 4500 volunteers all searching for these gigantic numbers, why not join us...... .....GIMPS Stands for the Great Internet Mersenne Prime Search, and is a world wide project involving over 4500 participants (@ September 1998), coordinated by George Woltman who maintains the GIMPS site and Scott Kurowski who runs the Primenet Internet Server . Every member of the group runs some Free Software Please note that this size of task would have previously only been possible on large Supercomputers such as the Cray that was used to verify this result, but by running the software on thousands of individual machines we can collectively surpass the power of even the most powerful supercomputer.

33. Mersenne Primes (2 Mar 05) The 42nd mersenne prime M25964951 is a 7816230digit number. (3.44M). The 41stmersenne prime M24036583 is a 7235733-digit number. (3.32M) http://math.exeter.edu/rparris/mersenne.html

Mersenne Primes (2 Mar 05) To learn about Mersenne primes, visit GIMPS or MathWorld Wincalc will calculate and display these huge numbers. If you want to be able to see all the digits of a particularly large Mersenne prime, but do not want to tie up your computer for a couple of days, you can download self-extracting zip files (which are not kept on this server): The 42nd Mersenne prime is a 7816230-digit number. (3.44M) The 41st Mersenne prime is a 7235733-digit number. (3.32M) The 40th Mersenne prime is a 6320430-digit number. (2.79M) The 39th Mersenne prime is a 4053946-digit number. (1.80M) The 38th Mersenne prime is a 2098960-digit number. (969K) The 37th Mersenne prime is a 909526-digit number. (435K) The 36th Mersenne prime is a 895932-digit number. (429K) The 35th Mersenne prime is a 420921-digit number. (216K) The 34th Mersenne prime is a 378632-digit number. (197K) The 33rd Mersenne prime is a 258716-digit number. (144K) The 32nd Mersenne prime is a 227832-digit number. (130K) Smaller Mersenne primes can be calculated more quickly than they can be downloaded.

34. Mersenne Prime - A Whatis.com Definition A Mersenne (also spelled Marsenne) prime is a specific type of prime number. The first few known values of n that produce mersenne primes are where n http://whatis.techtarget.com/definition/0,,sid9_gci788348,00.html

Search our IT-specific encyclopedia for: or jump to a topic: Choose a topic... CIO CRM Data Center Domino Enterprise Linux Enterprise Voice Exchange IBM S/390 IBM AS/400 Mobile Computing Networking Oracle SAP Security Small Medium Business SQL Server Storage Visual Basic Web Services Windows 2000 Windows Security Windows Systems Advanced Search Browse alphabetically: A B C D ... General Computing Terms Mersenne prime A Mersenne (also spelled Marsenne) prime is a specific type of prime number . It must be reducible to the form 2 n - 1, where n is a prime number. The term comes from the surname of a French monk who first defined it. The first few known values of n that produce Mersenne primes are where n n n n n n n n n = 61, and n With the advent of computers to perform number-crunching tasks formerly done by humans, ever-larger Mersenne primes (and primes in general) have been found. The quest to find prime numbers is akin to other numerical searches done by computers. Examples are the decimal expansions of irrational number s such as pi (the circumference-to-diameter ratio of a circle) or e (the natural logarithm base). But the 'next' (unknown today, known tomorrow) prime is more difficult to find than the 'next' digit in the expansion of an irrational number. It takes the most powerful computer a long time to check a large number to determine if it is prime, and an even longer time to determine if it is a Mersenne prime. For this reason, Mersenne primes are of particular interest to developers of strong

35. Mersenne Prime Numbers Indeed, at present only 42 mersenne prime numbers are known. They are obtainedby letting The largest prime number known is a mersenne prime number. http://www.math.utah.edu/~alfeld/math/mersenne.html

Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah Mersenne Prime Numbers Mersenne prime numbers are numbers of the form For m to be prime, p itself must be prime, but that is not sufficient. Indeed, at present only 42 Mersenne prime numbers are known. They are obtained by letting p Note that for example so that for p = 11 we do not obtain a prime number. The largest prime number known is a Mersenne prime number. Mersenne prime numbers have their own web site which is dedicated to a netwide search for Mersenne prime numbers and related tasks. Fine print, your comments, more links, Peter Alfeld, PA1UM [06-Aug-1999]

36. 40th Mersenne Prime Confirmed EARLIER REPORTS that a 40th mersenne prime had been found have now been The boffins have said the newly discovered mersenne prime is 2209960111, http://www.theinquirer.net/?article=12985

37. PlanetMath: Mersenne Numbers mersenne primes have a strong connection with perfect numbers. The currentlyknown mersenne primes correspond to $ n$ = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, http://planetmath.org/encyclopedia/MersenneNumbers.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... Random Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Mersenne numbers (Definition) Numbers of the form are called Mersenne numbers after Father Marin Mersenne, a French monk who wanted to discover which such numbers are actually prime . It can be easily shown that if is prime then is prime. Indeed, with factors Mersenne primes have a strong connection with perfect numbers The currently known Mersenne primes correspond to = 2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13,466,917 and the newly discovered number , and even newer number . In fact, the latest (as of

38. Mersenne Primes A mersenne prime is a prime number of the form 2 p 1, where p is a prime. This is only the 38th in the sequence of mersenne primes. http://www.jcu.edu/math/vignettes/mersenne.htm

Vignette 19 Mersenne Primes A prime number is an integer greater than 1 whose only positive divisors are 1 and the number itself. Thus, the numbers 2, 3, 5, 7, 11, 13, 17, ... are prime. In Vignette 2 , you saw an elementary proof that there are infinitely many prime numbers. It was also pointed out that there is no formula that will generate all primes in sequence. Because of this fact, both professional and amateur mathematicians have for years attempted to determine larger and larger prime numbers. Mersenne Primes Since no formula can generate all prime numbers, attention has turned to looking for prime numbers that have a specific form. One such form that has been explored a great deal is that of Mersenne primes , named for Marin Mersenne, a French monk who began the study of these numbers in the early 1600's. A Mersenne prime is a prime number of the form 2 p - 1, where p is a prime. For instance, 2 - 1= 3 is prime, 2 - 1 = 7 is prime, 2 - 1 = 31 is prime, and so on. Not all such numbers are prime, however; for example, 2 89 is not prime.

39. Mersenne Prime In fact, after an early clustering of mersenne primes for fairly small values of p, At the time of writing there are 40 known mersenne primes, http://www.daviddarling.info/encyclopedia/M/Mersenne_prime.html

Return to The Worlds of David Darling INDEX LATEST NEWS ARCHIVE ... Z entire Web this site Mersenne prime A prime number of the form 2 p - 1, where p is prime. A prime exponent is necessary for a Mersenne number to be prime but is not sufficient; for example, 2 -1 = 2,047 = 23 x 89. In fact, after an early clustering of Mersenne primes for fairly small values of p , further occurrences become increasingly rare. At the time of writing there are 40 known Mersenne primes, corresponding to values for p of 2; 3; 5; 7; 13; 17; 19; 31; 61; 89; 107; 127; 521; 607; 1,279; 2,203; 2,281; 3,217; 4,253; 4,423; 9,689; 9,941; 11,213; 19,937; 21,701; 23,209; 44,497; 86,243; 110,503; 132,049; 216,091; 756,839; 859,433; 1,257,787; 1,398,269; 2,976,221; 3,021,377; 6,972,593; 13,466,917; and 20,996,011; however, it isn't known if the current largest Mersenne prime is the fortieth in order of size because not all lower exponents have been checked. Mersenne primes rank among the largest of all known primes because they have a particularly simple test for primality, called the Lucas-Lehmer test The search for Mersenne primes has been going on for centuries. They are named after Marin

40. Mersenne Primes - Wikisource This page lists the first 30 mersenne primes (prime numbers on the form 2n1), 1 mersenne primes 1-12; 2 mersenne prime 13; 3 mersenne prime 14 http://wikisource.org/wiki/Mersenne_primes

Mersenne primes From Wikisource This page lists the first 30 Mersenne primes (prime numbers on the form 2 n −1), with all decimal digits written out. Contents Mersenne primes #1-12 Mersenne prime #13 Mersenne prime #14 Mersenne prime #15 ... edit Mersenne primes #1-12 edit Mersenne prime #13 edit Mersenne prime #14 edit Mersenne prime #15 edit Mersenne prime #16 edit Mersenne prime #17 edit Mersenne prime #18 edit Mersenne prime #19 edit Mersenne prime #20 edit Mersenne prime #21 edit Mersenne prime #22 edit Mersenne prime #23 edit Mersenne prime #24 edit Mersenne prime #25 edit Mersenne prime #26 edit Mersenne prime #27 edit Mersenne prime #28 edit Mersenne prime #29 edit Mersenne prime #30 Retrieved from " http://wikisource.org/wiki/Mersenne_primes Categories Mathematics Views Article Discussion Edit History Personal tools Create an account or log in Navigation Main Page Community portal Scriptorium Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 08:47, 18 May 2005. Content is available under GNU Free Documentation License About Wikisource

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