21. Mersenne Prime Search | MetaFilter Mersenne Prime Search is a distributed computing project much like Seti@home, except instead of searching for aliens, you're in the running for $100,000 and a place in math history http://www.metafilter.com/2381/

skip to main content MetaFilter AskMeFi Projects ... New User Tags: distributedcomp math mathematics Mersenne ... PrimeNumbers Mersenne Prime Search July 7, 2000 9:53 AM Subscribe Mersenne Prime Search is a distributed computing project much like Seti@home , except instead of searching for aliens, you're in the running for $100,000 and a place in math history (shouldn't your computer actually be the one that goes into the math history books?). posted by mathowie (1 comment total) This is terribly exciting to me, but how can I choose between having my computer search for aliens, and search for numbers. I have a bunch of old mac's and pc's lying around, it might be time to press them back into service. posted by thirteen at 11:51 AM on July 7, 2000 This thread has been archived and is closed to new comments Related Posts from complexity, universality October 24, 2010 Mathematics Illuminated April 14, 2010 The Grey Lady teaches Math April 11, 2010 Prime Prize April 12, 2007 Find a 10 million digit prime number, May 18, 2001 Features Login New User Links Home Archives Tags About Sites MetaFilter AskMeFi Projects Music ... MetaFilter Network Inc.

22. Ricerca Dei Numeri Primi Di Mersenne Questa pagina illustra parte della matematica e degli algoritmi utilizzati per una ricerca dei numeri primi di Mersenne. http://www.moreware.org/mersenne/prime-it.htm

CPU Benchmarks Agosto/Settembre 2008 : - Nuovi Primi di Mersenne Pagine disponibili in Olandese Francese Tedesco Inglese ... Cinese . Attenzione: Alcune traduzioni potrebbero non essere aggiornate - usare AltaVista se necessario. 45mo e 46mo Numero Primo di Mersenne finalmente scoperti!!!! GIMPS pronto a richiedere il premio di $100,000 della EFF ! Scarica il software Il 23 Agosto, un computer dell'UCLA (University of California, Los Angeles) ha scoperto il 45mo primo di Mersenne noto, 2 -1, un numero mammuth da 12.978.189 cifre ! Il numero primo beneficia del premio da $100.000 offerto dalla Electronic Frontier Foundation Hans-Michael Elvenich il 46th primo di Mersenne, 2 -1, un numero da 11,185,272 cifre ! Si tratta del primo numero primo di Mersenne scoperto in ordine non sequenziale da quando Colquitt e Welsh scoprirono 2 -1 nel 1988. In riconoscimento degli scopritori, dei capi progetto GIMPS e dei contributi di ciascun partecipante del progetto GIMPS, il credito per i due primi andrà a "Edson Smith, George Woltman, Scott Kurowski, et al." e "Hans-Michael Elvenich, George Woltman, Scott Kurowski, et al.". Hans-Michael Elvenich è un ingegnere elettrico di 44 anni che lavora per Aliseca, un'indistria chimica. Egli è uno studioso dei numeri primi, nonché proprietario e gestore di www.primzahlen.de. In tedesco, numeri primi si traduce con "Primzahlen".

23. What Is A Mersenne Prime Number? Sep 9, 2010 Brief and Straightforward Guide What is a Mersenne Prime Number? http://www.wisegeek.com/what-is-a-mersenne-prime-number.htm

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

TEAM PRIME RIB Home Chat Room guide TPR Seventeen or Bust 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 : 02-Feb-2006 00:47 UTC (Feb 01 2006 19:47 EST) Last Primenet Report Date : 02-Feb-2006 00:00 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 aEric 29-Jan-06 29-Jan-06 Baenwort Baenwort 29-Jan-06 riskin 29-Jan-06 27-Jan-06 Exponents due to expire within 14 days Exponent Type Bits Iteration Days Date Computer Id Member Run Expiry Updated Assigned L 03-Dec-05 14-Nov-05 tom L 07-Dec-05 07-Dec-05 L 07-Dec-05 07-Dec-05 L 07-Dec-05 L 07-Dec-05 L 07-Dec-05 L 07-Dec-05 L 07-Dec-05 L 07-Dec-05 D 07-Dec-05 06-Dec-05 robcreid D 07-Dec-05 30-Nov-05 robcreid D 07-Dec-05 24-Nov-05 robcreid D 10-Dec-05 30-Oct-05 Bill D 11-Dec-05 04-Dec-05 whilden L 11-Dec-05 01-Dec-05 RidaVids D 08-Dec-05 26-Nov-05 L 16-Nov-05 25-Oct-05 Cobi L 14-Dec-05 12-Dec-05 L 15-Dec-05 29-Oct-05 Ridavids L 15-Dec-05 26-Nov-05 Ridavids L 16-Dec-05

25. Mersenne Prime: Definition From Answers.com A Mersenne number that is also a prime number. http://www.answers.com/topic/mersenne-prime

26. Prime Numbers Prime Numbers. Largest known Mersenne prime. Mersenne primes are primes of the form 2^p 1. For 2^p - 1 to be prime we must have that p is prime. http://www.cs.uwaterloo.ca/~alopez-o/math-faq/mathtext/node10.html

Next: Special Numbers and Functions Up: Number Theory Previous: Fermat's Last Theorem Prime Numbers Largest known Mersenne prime Mersenne primes are primes of the form 2^p - 1 . For 2^p - 1 to be prime we must have that p is prime. is prime. It was discovered in 1997. Largest known prime The largest known prime is the Mersenne prime described above. The largest known non-Mersenne prime, is , discovered by Brown, Noll, Parady, Smith, Smith, and Zarantonello. You can help find more primes. For more information see: The Great Internet Mersenne Prime Search home page on http://www.mersenne.org References Brown, Noll, Parady, Smith, Smith, and Zarantonello. Letter to the editor. American Mathematical Monthly, vol. 97, 1990, p. 214. Largest known twin primes The two largest known twin primes are . with 11713 digits, found by Indlekofer and Ja'rai in November, 1995. They are also the first known gigantic twin primes (primes with at least 10,000 digits). Recent record holders are: , with 5129 digits, by Harvey Dubner. , with 4932 digits, found by Indlekofer and Ja'rai in 1994.

27. The Largest Known Primes The largest known prime has almost always been a Mersenne prime. http://primes.utm.edu/largest.html

The Largest Known PrimesA Summary (A historic Prime Page resource since 1994!) Last modified: 07:50:30 Sunday October 31 2010 UTC Our book " Prime Curios! The Dictionary of Prime Number Trivia " is now available on CreateSpace Amazon 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 . The site The Top Twenty is a greatly expanded version of this information. This page summarizes the information on the list of 5000 Largest Known Primes updated hourly ). The complete list of is available in several forms 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

28. The Prime Glossary: Mersenne Prime Welcome to the Prime Glossary a collection of definitions, information and facts all related to prime numbers. This pages contains the entry titled 'Mersenne prime.' http://primes.utm.edu/glossary/xpage/Mersennes.html

Mersenne prime (another Prime Pages ' Glossary entries) Glossary: Index Search Home Previous ... Mail Editor Prime Pages: Home Search Index FAQ Top 5000: Primes Provers Curios A Mersenne number n -1 which is prime is called a Mersenne prime . If m divides n , then 2 m -1 divides 2 n -1, so a Mersenne prime has a prime exponent. However, very few of the numbers of the form 2 p p prime) are prime. Mersenne Numbers are the easiest type of number to prove prime (because of the Lucas-Lehmer test), so are usually the largest primes on the list of largest known primes). Primes of this form were first studied by Euclid who explored their relationship with the even perfect numbers . They were named after Mersenne because he wrote to so many mathematicians encouraging their study and because he sparked the interest of generations of mathematicians by claiming in 1644 that M p was prime for 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257 and for no other primes p less than 257. It took three centuries to completely test his bold claim, and when done, it was discovered that he was wrong about M and M being prime, and he omitted M

29. Mersenne Prime for an Integer to be Prime, must be Prime. This is true since for Composite with factors and , . Therefore, can be written as , which is a Binomial Number and can be factored. http://www.math.sdu.edu.cn/mathency/math/m/m194.htm

Mersenne Prime A Mersenne Number which is Prime is called a Mersenne prime. In order for the Mersenne number defined by for an Integer to be Prime must be Prime . This is true since for Composite with factors and . Therefore, can be written as , which is a Binomial Number and can be factored. Every Mersenne Prime gives rise to a Perfect Number If is a Prime , then Divides Iff is Prime . It is also true that Prime divisors of must have the form where is a Positive Integer and simultaneously of either the form or (Uspensky and Heaslet). A Prime factor of a Mersenne number is a Wieferich Prime Iff , Therefore, Mersenne Primes are not Wieferich Primes . All known Mersenne numbers with Prime are Squarefree . However, Guy (1994) believes that there are which are not Squarefree Trial Division is often used to establish the Compositeness of a potential Mersenne prime. This test immediately shows to be Composite for , 23, 83, 131, 179, 191, 239, and 251 (with small factors 23, 47, 167, 263, 359, 383, 479, and 503, respectively). A much more powerful primality test for is the Lucas-Lehmer Test It has been conjectured that there exist an infinite number of Mersenne primes, although finding them is computationally very challenging. The table below gives the index

30. Main Page - Mersennewiki Information about the Great Internet Mersenne Prime Search, other distributed prime projects, and the related mathematics. http://mersennewiki.org

Main Page From Mersennewiki Welcome to the Mersenne Wiki. This wiki is about the Great Internet Mersenne Prime Search (GIMPS), a distributed computing project dedicated to finding Mersenne primes . However, information about related projects may also be contributed, expanding any of the 216 existing articles or creating new ones. edit To all users! Please remember to create an account and log in to edit pages. You can play around in the Sandbox Unfortunately, account creation by new users is now disabled due to excessive spam. However, anyone desiring editing status can request an account on the GIMPS forum. edit Categories Some pages on this wiki have been categorized edit Mathematics Frequently asked questions Glossary Factorization methods Primality tests ... edit Software GIMPS clients - includes the official GIMPS clients Prime95 and MPrime edit Hardware Frequently asked questions edit Projects GIMPS 100 Million Digit Prefactor Project 12121 Search 15k Search ... Aliquot Sequences Search (see also: this subforum in the mersenneforum ElevenSmooth Cunningham Tables Twin Prime Search ... edit Contributors (Feel free to post your name here and eventually what you've done) OmbooHankvald - Making guides, writing wiki, simplifying advanced stuff.

31. [Prime] It's Official - 47th Mersenne Prime Found The verification just finished. M42643801 is the 47th known Mersenne prime! It is not quite as big as the Mersenne prime found last August. Percentagewise M42643801 and M43112609 http://www.mail-archive.com/prime@hogranch.com/msg02379.html

prime Thread Date [Prime] It's official - 47th Mersenne Prime found George Woltman Fri, 12 Jun 2009 12:48:15 -0700 http://hogranch.com/mailman/listinfo/prime [Prime] It's official - 47th Mersenne Prime found George Woltman Re: [Prime] It's official - 47th Mersenne Prime found david eddy Re: [Prime] It's official - 47th Mersenne Prime found Steinar H. Gunderson Re: [Prime] It's official - 47th Mersenne Prime found Steven J Phipps Re: [Prime] It's official - 47th Mersenne Prime found Rodolfo Ruiz Huidobro Reply via email to

32. What Is Mersenne Prime? Definition From WhatIs.com A Mersenne (also spelled Marsenne) prime is a specific type of prime number. It must be reducible to the form 2 to the nth power 1, where n is a prime number. http://whatis.techtarget.com/definition/0,,sid9_gci788348,00.html

Mersenne prime HOME SEARCH BROWSE BY CATEGORY BROWSE BY ALPHABET ... WHITE PAPERS Search our IT-specific encyclopedia for: Browse alphabetically: A B C D ... Computing Fundamentals 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' 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 encryption methods.

33. Integer Lists: Mersenne Primes The great Mersenne Prime race has been in progress now for over 600 years and . GIMPS Great Internet Mersenne Prime Search for the complete listing, http://www.tsm-resources.com/alists/mers.html

MERSENNE PRIMES Mersenne Primes are of the form , where p is itself prime. The search was on when it was noticed that most of the early primes worked, but 2^11-1 was not prime. The great Mersenne Prime race has been in progress now for over 600 years and shows no sign of ending. Some of the more reasonably sized numbers are given in this list together with the date of discovery. Who was Mersenne? Java Applet (1) - finds factors of all positive integers up to Java Applet (2) - finds factors of all positive integers up to History of Prime discoveries Return to Integer Lists menu : by pure brain-power - 2^11-1 = 2047 = 23 x 89 = 8191 .. .. .. .. .. .. .. [proved 1456] = 131071 .. .. .. .. .. .. .. [proved 1588, Cataldi] = 524287 .. .. .. .. .. .. .. [proved 1588, Cataldi] - 2^23-1 = 8388607 = 47 x 178481 - 2^29-1 = 536870911 = 233 x 1103 x 2089 = 2147483647 .. .. .. .. .. .. .. [proved 1772, Euler]

34. The UCLA Mersenne Prime In August of 2008, a new Mersenne Prime number was discovered on one of the computers belonging to the UCLA Mathematics Department's Program in Computing (PIC). http://www.math.ucla.edu/~edson/prime/

The UCLA Mersenne Prime In August of 2008, a new Mersenne Prime number was discovered on one of the computers belonging to the UCLA Mathematics Department's Program in Computing (PIC) . This number turns out to be the World's Largest known prime number, and the discovery has generated a lot of interest. In an effort to save everyone time and energy, I thought I'd put some information up on the web in FAQ format. Since a number of the questions I've received have come from people with non-technical backgrounds (including children), this FAQ is non-technical. You do have to know what a Prime Number is, though. I am compelled, though, to offer this caveat: even though I work for the Mathematics Department, I'm a System Administrator, not a Mathematician! If you're looking for serious Mersenne Prime information, I refer you to Chris Caldwell's excellent web site Mersenne Primes: History, Theorems and Lists. Other interesting sites include Wolfram's Mersenne Prime page and Landon Curt Noll's entertaining Mersenne Prime Digits and Names Now, on to the questions!

35. PlanetMath: Table Of Mersenne Primes The number 1 has been left off this listing, not out of some dogmatic belief that it is not a prime number, but because accepting it as a Mersenne prime one would have to also http://planetmath.org/encyclopedia/TableOfMersennePrimes.html

(more info) Math for the people, by the people. donor list find out how Encyclopedia Requests ... Advanced search Login create new user name: pass: forget your password? Main Menu sections Encyclopædia 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 table of Mersenne primes (Data Structure) This is a table of the known Mersenne primes . This table could be complete , but it could just as easily be hopelessly short of completeness. The first few Mersenne primes are so small written in base 10 that there is no excuse not to do so. Furthermore, since these were known since antiquity and the name of the first discoverer can be neither ascertainted nor disputed, we can dispense with the ``Discoverer'' field and instead use it for the associated perfect number (or 2-perfect number , to be more precise, see: multiply perfect number ). The first field gives the rank (the Mersenne prime's position in A000396 of Sloane's OEIS ), the second field gives the

36. PrimeNet 5.0 PrimeNet is a distributed computing project for the Great Internet Mersenne Prime Search, co-ordinating the assignment of work and collection of results. http://www.mersenne.org/primenet/

Great Internet Mersenne Prime Search PrimeNet 2010-10-31 08:01:00 utc Login Password forgotten? Getting Started! Create Account Download Software ... Legal Today's Numbers Teams 381 Users 51890 CPUs 345771 TFLOP/s 41.085 GHz-Days 20542.349 Hosting provided by SBSI Managed Services PrimeNet Activity Summary 2010-10-31 07:00 UTC Stats updated in the first minutes of every hour Aggregate Computing Power Today, last 24 hours Week, last 7 days Month, last 30 days Potential TFLOP/sec Actual TFLOP/sec Potential TFLOP/sec Actual TFLOP/sec Potential TFLOP/sec Actual TFLOP/sec Power GHz-Days Power GHz-Days Power GHz-Days Resources Registered teams user IDs computers work units Recently Active and Work Done Resource 24 hours 7 days 30 days user IDs computers work units Exponent Status Distribution You are visitor number since August 1, 1996 courtesy of WebCounter. (c)1996-2010 Mersenne Research, Inc.

37. Mersenne Prime Numbers - MersennePrimes.com - Prime And Mersenne Numbers Spring, 2009 Norwegian mathematician finds 47th Mersenne prime, nearly 13 million digits long! He was aided by GIMPS (read about that group here). http://www.mersenneprimes.com/

What is a Mersenne Prime Math doesn't make worldwide news very often, but sometimes we hear about mathematicians finding a new super-large prime number. Those numbers are usually a type called Mersenne primes News Flash! Spring, 2009: Norwegian mathematician finds 47th Mersenne prime , nearly 13 million digits long! He was aided by GIMPS (read about that group here ). See National Public Radio coverage of the story Here is a brief introduction to this little-known branch of number theory. Prime numbers First, be sure you know what a prime number is. It is a number that has exactly two factors (numbers that "go into" it with no remainder): 1 and itself.

38. Mersenne Primes And Fermat Primes Math reference, Mersenne prime, Fermat prime. Numbers, Mersenne Primes and Fermat Primes Mersenne Primes A Mersenne prime is a prime that is one less than a power of 2. http://www.mathreference.com/num,mers.html

Numbers, Mersenne Primes and Fermat Primes showHeader(4, "", "num", "Number Theory", ""); Mersenne Primes A Mersenne prime is a prime that is one less than a power of 2. Examples include 3, 7, and 31. The exponent on a Mersenne prime must also be prime. To illustrate, consider 2 -1. Now 15 is not prime, infact it is 3×5, so replace 2 with 8, and write 8 -1. This is divisible by 8-1, just as x n -1 is divisible by x-1. If p is a Mersenne prime, say 2 k -1, then consider n = p×2 k-1 k k-1 . This is equal to 2 k k ×p, which is twice n, hence n is a perfect number. Perfect numbers include 6, 28, and 496, corresponding to the first three Mersenne primes. k k k , n becomes abundant. Any additional factors, besides 2 and j, will also make n abundant. Therefore all perfect even numbers have been characterized. They correspond one to one with the Mersenne primes. No perfect odd numbers have been found. Fermat Primes A Fermat prime is one greater than a power of 2. Examples include 3, 5, 17, 257, and 65537. Consider the number 2 h ×n) h , then our fermat prime can be written as x n +1, which is divisible by x+1. To be prime, n must equal 1, whence the exponent is a power of 2. Review the 5 examples above. Each is 2 to a power of 2, plus 1. In fact, these are the only known Fermat primes, and we believe there are no others.

39. Ars Technica Team Prime Rib Information, statistics, FAQs, and chat room on how they support the Mersenne Prime Search. http://www.teamprimerib.com/rr1/

40. Mersenne Prime Numbers - MersennePrimes.com - Finding Prime Numbers An introduction to Mersenne prime numbers. http://www.mersenneprimes.com/Finding-Prime-Numbers.html

Finding Prime Number s It's easy to write a computer program to find prime numbers. In the late 1990's, while teaching middle-school math, I wrote a program (in the Basic language) that ran on my ancient [pre-Windows] IBM laptop. Here are the principles it followed: Take an odd number (call it x ). For example, if you already know the prime numbers up to 10, you can start with x = 11. (We don't have to test even numbers, since every even number greater than 2 is composite, with at least three factors [1, 2, and itself].) Find out whether 3 is a factor of x, by seeing whether ( x /3) is an integer. If 3 is a factor of x, then start testing the next odd number, x +2, to see if it is prime. (I didn't have to check any even numbers above 2, because they are all composite.) If 3 is not a factor of x, add two to it and try again: that is, see whether 5 is a factor of x. (Since all of my possible prime numbers above 2 were odd, I didn't have to test whether even numbers were factors of those odd numbers; the answer would always be no.) Keep adding two to the possible factor until it gets larger than the square root of x . If none of those numbers is a factor of x

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