61. The Great Internet Mersenne Prime Search A mersenne prime is a Mersenne number which is prime. Gimps connects the pureresearch of finding new mersenne primes with the technology of the computer. http://www.math-cs.cmsu.edu/~gimps/gimps.html

The Great Internet Mersenne Prime Search GIMPS , founded by George Woltman in January of 1996, is dedicated to the rigorous search for new Mersenne primes. A Mersenne number is any number of the form 2 p - 1 where p is a prime. A Mersenne prime is a Mersenne number which is prime. Gimps connects the pure research of finding new Mersenne primes with the technology of the computer. The goal of GIMPS is to test the primality of every Mersenne number with an exponent less than 20,500,000. GIMPS uses a program written by Woltman that implements the Lucas-Lehmer Test and multiplies using Fast Fourier Transforms along with network software and the PrimeNet server developed by Scott Kurowski and the company Entropia . Over 12,000 number theory enthusiasts have harnessed thousands of small computers to search for these huge prime numbers using Woltman's program. GIMPS has now found the four largest known Mersenne primes. The following list gives these four Mersenne primes, their discoverer, and the date of their discovery. -1 Joel Armengaud, George Woltman, GIMPS November 13, 1996

62. *Concerns Of Young Mathematicians* || New Mersenne Prime Discovered The Great Internet mersenne prime Search has discovered a new mersenne prime, New mersenne prime Discovered 0 comments (0 topical, 0 editorial, http://concerns.youngmath.net/story/2005/3/2/22439/39508

The Young Mathematicians' Network Serving the Community of Young Mathematicians Sections: Front Page News Grad Life Undergrad Life ... All New Mersenne Prime Discovered Research By overconvergent Posted Wed Mar 2nd, 2005 at 02:24:39 PDT The Great Internet Mersenne Prime Search has discovered a new Mersenne Prime, Post a Comment Child Care on Campus The Moore Method (0 comments) Display: Threaded Minimal Nested Flat Sort: Unrated, then Highest Highest Rated First Lowest Rated First Ignore Ratings Newest First Oldest First New Mersenne Prime Discovered comments (0 topical, editorial, hidden) Display: Threaded Minimal Nested Flat Sort: Unrated, then Highest Highest Rated First Lowest Rated First Ignore Ratings Newest First Oldest First Menu Submit a Story create account FAQ Search ... Recent Comments Login Make a new account Username: Password: Related Links Great Internet Mersenne Prime Search Also by overconvergent submit story create account ... search

63. The Mersenne Primes The mersenne primes. by Stu Savory, 22/2/2005. A mersenne prime is a Mersennenumber, ie, a number of the form M=2n1 which is prime. http://home.egge.net/~savory/maths13.htm

The Mersenne Primes by Stu Savory, 22/2/2005. A Mersenne prime is a Mersenne number, i.e., a number of the form M=2 n -1 which is prime. In order for M=2 n -1 to be prime, n must itself be prime, and not e.g. 15 (=3*5) or 63 (=3*3*7) which are composite. For composite n with factors r and s, we have n = rs. Therefore, M=2 n -1 is M=2 rs -1 , which is a binomial which always has factors (2 s r +1) and so is NOT prime (Q.E.D) As of 22/2/2005 the 42nd Mersenne Prime has (probably) been discovered. Confirmation still needed. The currently known Mersenne Primes are :- <10000000 2005 GIMP ======================================================================== Now go visit my blog please :-) Index/Home Impressum Sitemap Search

64. Numcom09 Before we define what a mersenne prime is, we need to explain the meaning of A mersenne prime is a prime number of the form 2^n 1 named after the monk http://www.eng.um.edu.mt/~andebo/numbers/numcom09.htm

NUMBERS AND COMPUTERS (9) by Albert N. Debono MERSENNE PRIMES Since we are discussing primes again perhaps we should repeat the definition of a prime number. A prime is a whole number greater than 1, whose only exact divisors are 1 and the number itself. Thus 2, 3, 5, 7, 11, 13 are primes whereas 4, 6, 8, 9, 10, 12, 14, 15 are not. Refer to Numbers and Computers (4) for hints on how to write a computer program to find them. The number of primes is infinite and 2 is the only even prime. Back to list of articles.

65. Largest Known Mersenne Prime Largest known mersenne prime. Largest known mersenne prime. mersenne primesare primes of the form . For to be prime we must have that p is prime. http://db.uwaterloo.ca/~alopez-o/math-faq/node28.html

Next: Largest known prime Up: Prime Numbers Previous: Prime Numbers Largest known Mersenne prime Mersenne primes are primes of the form . For to be prime we must have that p is prime. is prime. It was discovered in 1997. Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

66. What Is The Current Status On Mersenne Primes? What is the current status on mersenne primes? The following mersenne primesare known. The way to determine if is prime is to use the LucasLehmer test http://db.uwaterloo.ca/~alopez-o/math-faq/node35.html

Next: Formulae to compute prime Up: Prime Numbers Previous: List of record numbers What is the current status on Mersenne primes? The following Mersenne primes are known. The way to determine if is prime is to use the Lucas-Lehmer test: Lucas_Lehmer_Test(p): u := 4 for i from 3 to p do u := u^2-2 mod 2^p-1 od if u == then 2^p-1 is prime else 2^p-1 is composite fi All exponents less than 1,481,800 have now been tested at least once. References An introduction to the theory of numbers. G.H. Hardy, E.M. Wright. Fifth edition, 1979, Oxford. Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

67. Generalized Fermat Primes Search Today, all the mersenne primes having less than 2000000 digits are known and But the Fermat and mersenne primes are rare and the chance to find a new http://perso.wanadoo.fr/yves.gallot/primes/

Home News How ? Download ... Feedback Welcome to the Generalized Fermat Prime Search! During the 17 th century, Pierre de Fermat and Marin Mersenne studied two particular forms of numbers, thinking that they could produce a large amount of prime numbers or even to be ever prime. Mersenne communicated a list of the primes of the form 2 n -1, for all n n is a power of 2, then 2 n +1 is a prime. Fermat knew that 3, 5, 17, 257 and 65537 are primes but later Euler showed that Fermat's conjecture is false by discovering a factor to the next number. In honour of the inspired pioneers, the numbers of the form 2 n -1 are now called the Mersenne numbers and the numbers of the form 2 n +1 the Fermat numbers. The search for Mersenne and Fermat primes has been greatly extended since the 17 th century. Today, all the Mersenne primes having less than 2,000,000 digits are known and all the Fermat primes up to 2,000,000,000 digits! It was possible because during the 19 th century some efficient tests were discovered to check the primality of these numbers. But at the same time, some tests as fast were also found to test check the primality of all the numbers

68. Mersenne Prime Numbers GIMPS (the Great Internet mersenne prime Search) is a distributed computingproject that is systematically testing possible candidates to find Mersenne http://www2.potsdam.edu/millerrs/Mersenne.html

Roger's Homepage Team Stats Team Performnce Join Team ... Brian's Site Mersenne prime numbers are a special class of prime numbers that have the form, . A necessary condition for this number to be prime is that p is also prime. Out of all the tested exponents, only 39 Mersenne primes have been identified. It is an open question whether there is a finite or infinite number of primes of this form. GIMPS (the Great Internet Mersenne Prime Search) is a distributed computing project that is systematically testing possible candidates to find Mersenne Primes. Brian Jue , Assistant Professor of Mathematics at CSU Stanislaus, coordinates a team to participate in the search. Computers in the Math, Physics, and Chemistry Departments, some of the campus computer labs and many student computers have been recruited for the project. The program runs in the background at the lowest priority, so it doesn't interfere with any other tasks or degrade system performance. You can see how the team is doing by clicking on Team Stats . Click on Join Team to find out how you can contribute your spare computer cycles. For more information contact

69. 39th Mersenne Prime Discovered Announcing the discovery of the 39th mersenne prime. http://alpha01.dm.unito.it/personalpages/cerruti/primi/primigrandi/39.html

Researchers Discover Largest Multi-Million-Digit Prime Using Entropia Distributed Computing Grid. -1 is now the Largest Known Prime. SAN DIEGO, California and ORLANDO, Florida, December 6, 2001 Michael Cameron, a 20 year-old volunteer in a worldwide research project called the Great Internet Mersenne Prime Search (GIMPS) , has discovered the largest known prime number using his PC and software by George Woltman and Entropia, Inc. as part of an international grid of more than 205,000 interconnected computers operated by the company. The new number, expressed in shorthand as 2 -1, contains 4,053,946 digits and was discovered November 14th. It belongs to a special class of rare prime numbers called Mersenne primes . The discovery marks only the 39th known Mersenne prime, named after Marin Mersenne , a 17th century French monk who studied the numbers. Mersenne primes are most relevant to number theory, but most participants join GIMPS simply for the fun of having a role in real research - and the chance of finding a new Mersenne prime. Cameron used a 800 MHz AMD T-Bird PC running part-time for 45 days to prove the number prime. He said, "A friend informed me that if I was going to leave my computer on all the time I should make use of that wasted CPU time. I put GIMPS on my PC because it does not interfere with my work on the computer. Finding the new prime was a wonderful surprise!"

70. Isabel’s Math Blog » 42nd Mersenne Prime Discovered It’s the 42nd known mersenne prime. Note that there is a rather efficient mersenne primes are distributed such that M(n) = the nth mersenne prime grows http://www.izzycat.org/math/index.php?p=91

71. Mersenne Primes Author yendor Could someone please explain mersenne primes to me, examples, likethe smallest mersenne prime which is not a prime number, also is there any http://www.newton.dep.anl.gov/newton/askasci/1995/math/MATH037.HTM

Ask A Scientist Mathematics Archive Mersenne primes Back to Mathematics Ask A Scientist Index NEWTON Homepage Ask A Question ... NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators. Argonne National Laboratory, Division of Educational Programs, Harold Myron, Ph.D., Division Director.

72. The 32nd Mersenne Prime, Predicted By Anonymous The 32nd mersenne prime, Predicted by Anonymous a free ebook from manybooks.net.Read on your PDA, Cellphone, iPod, or eBook reader! http://www.manybooks.net/titles/anonetext9332pri10.html

@import "/resources/2005.css"; Content Navigation Footer Search - advanced search Title Author Authors Titles Categories Languages ... Help The 32nd Mersenne Prime, Predicted Author Anonymous Categories Reference Non-fiction Language English Excerpt Reviews Be the first to review this title! Download select format... PDF eReader Doc Plucker zTXT . iSilo . iSiloX . Rocketbook . TCR . iPod Notes . Librie [beta] . Total downloads: 26 Support manybooks with a small donation More eBooks by Anonymous: 32nd Mersenne Prime, Predicted, The After Long Years Aladdin and the Magic Lamp Aljaska en de Canada-spoorweg ... American Goliah, The Additional Links Anonymous at Wikipedia.org Read online (118.5 pages) Site links About manybooks.net Contact Webmaster RSS feed Admin access

73. Mersenne Primes: History, Theorems And Lists Definition When 2^n1 is prime it is said to be a mersenne prime. The listof all known primes p for which M(p) is a mersenne prime (therefore P(p) is http://cage.rug.ac.be/~hvernaev/mersenne.shtml

Mersenne Primes: History, Theorems and Lists 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 Remote pages on Mersennes: Marin Mersenne, the man Summary of the Status of the Search for Mersenne Primes Primes: [ Home Largest Finding How Many? ... Guestbook 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 2^11-1 = 2047 was not prime (it is 23*89). By 1603 Pietro Cataldi had correctly verified that 2^17-1 and 2^19-1 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

74. Mersenneforum.org - Great Internet Mersenne Prime Search SubForums Great Internet mersenne prime Search, Search this Forum mersenne prime Search, Software, Math, Hardware, Data, Marin s Mersenne-aries http://mersenneforum.org/forumdisplay.php?f=24

75. Jim's Prime Page The first few prime numbers are 2, 3, 5, 7, and 11. A mersenne prime is a primenumber that is one less than a power of two. That is, a number of the form http://home.netcom.com/~jrhowell/math/prime.htm

My Page about Prime Numbers This page uses sub scripts and super subscripts and superscipts in this sentence, you may have difficulty reading this page. The Great Internet Mersenne Prime Search On February 18, 2005, GIMPS, the , found its eighth Mersenne Prime, namely: which has 7,816,230 digits. For more details, see the GIMPS announcement Previously, GIMPS found the Mersenne primes: (7,235,733 digits) on May 15, 2004. For more details, see the GIMPS announcement (6,320,430 digits) on November 17, 2003. For more details, see the GIMPS announcement (4,053,946 digits) on November 14, 2001. For details, see the GIMPS announcement (2,098,960 digits) on June 1, 1999. This was the first known prime number with more than 1,000,000 digits. For details, see the GIMPS announcement (909,526 digits) in January, 1998. (895,932 digits) in August, 1997. (420,921 digits) in November, 1996. I have participated in GIMPS since about September of 1996. For more information on GIMPS, including how you can join the search, see the Mersenne Prime web site . This site also has links to other math-oriented projects. More about Prime Numbers A prime number is a number greater than 1, that is divisible only by itself and 1. The first few prime numbers are: 2, 3, 5, 7, and 11.

76. Off The Kuff: New Mersenne Prime Found 17, when he glanced at the screen and saw New mersenne prime found. The discovery of a new mersenne prime also means that we have discovered a new http://www.offthekuff.com/mt/archives/002724.html

Off the Kuff Knowledge Is Good in the Reality-Based Community Contact me: kuff - at - offthekuff.com Main December 11, 2003 New Mersenne prime found I love stories about big prime numbers More than 200,000 computers spent years looking for the largest known prime number. It turned up on Michigan State University graduate student Michael Shafer's off-the-shelf PC. "It was just a matter of time," Shafer said. The number is 6,320,430 digits long and would need 1,400 to 1,500 pages to write out. It is more than 2 million digits larger than the previous largest known prime number. Shafer, 26, helped find the number as a volunteer on an eight-year-old project called the Great Internet Mersenne Prime Search. Tens of thousands of people volunteered the use of their PCs in a worldwide project that harnessed the power of 211,000 computers, in effect creating a supercomputer capable of performing 9 trillion calculations per second. Participants could run the mathematical analysis program on their computers in the background, as they worked on other tasks. Shafer ran an ordinary Dell computer in his office for 19 days until Nov. 17, when he glanced at the screen and saw "New Mersenne prime found."

77. [Prime] 41st Mersenne Prime Reported! For mersenne primes, the best we have is a heuristic argument which predicts aninfinite number of mersenne primes the predicted distribution for http://hogranch.com/pipermail/prime/2004-May/000019.html

[Prime] 41st Mersenne Prime reported! gann at mailblocks.com Mon May 17 16:19:54 PDT 2004 Previous message: [Prime] 41st Mersenne Prime reported! Next message: [Prime] 41st Mersenne Prime reported! Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] They are "infinite" and "few" at the same time? ;) http://MILLIBIT.com http://GANNS.com like_dbaguy at hotmail.com prime at HOGRANCH.COM From: "Brian J. Beesley" < bjb at bbhvig.uklinux.net prime at hogranch.com prime at hogranch.com Subject: Re: [Prime] 41st Mersenne Prime reported! Date: Mon, 17 May 2004 06:36:02 +0000 On Monday 17 May 2004 04:58, you wrote: infinite number of Mersenne numbers with prime exponents which are _composite_ - an assertion which, at first sight, seems much more obvious. If it were to turn out that there are a finite number of composite prime-exponent Mersenne numbers, then it would automatically follow that been possible to "prove a negative". Which is true enough - though a single positive observation disproves that theory.

78. Explananda: 41st Mersenne Prime Found? The discovery of the 41st mersenne prime would also mean the discovery of the41st perfect number. Update After finding the message boards where the http://www.explananda.com/archives/000195.html

Main May 15, 2004 41st Mersenne prime found? Posted by Spencer MathWorld is reporting that a computer participating in GIMPS , the Great Internet Mersenne Prime search, claims to have found the 41st Mersenne prime this morning. This would be the largest known prime number, with roughly 7 million digits. There's a $100,000 prize for the discovery of the first prime with 10 million digits, which GIMPS is likely to claim within a couple years. The discovery of the 41st Mersenne prime would also mean the discovery of the 41st perfect number Update: After finding the message boards where the discovery is being discussed, it looks quite possible that there has been a new Mersenne prime found, but that it might be smaller that a previously known Mersenne prime. Posted by Spencer at May 15, 2004 01:38 PM Comments var site="s15Explananda" This work is licensed under a Creative Commons License

79. 40th Mersenne Prime Is Discovered 42nd mersenne prime Found by GIMPS and Announced MidFebruary 2005 It wasfound as part of the Great Internet mersenne prime (GIMP) Search. http://members.aol.com/DrMWEcker/Mersenne.htm

nd Mersenne Prime Found by GIMPS and Announced Mid-February 2005 Details by Dr. Mike Ecker, REC Editor I learned of this discovery around 18 February 2005. This is the third Mersenne found in 1 ¼ years (as announced in earlier issues of REC), so others and I are not giving it as much play as in the past. The new prime is 2 – 1, the largest known prime to date, and contains 7,816,230 million digits. I verified the number of digits with my QBASIC program, Digitcnt.BAS, repeated below: CLS : PRINT "Dr. Mike Ecker's program to calculate the number of digits of a^n": PRINT DO: a = 0: n = WHILE a <= OR a <> INT(a): INPUT "What is the (positive integer) base, a"; a: WEND WHILE n <= OR n <> INT(n): INPUT "What is the (positive integer) power, n"; n: WEND digits = INT(n * (LOG(a) / LOG(10))) + 1: REM Convert log base e to log base 10 PRINT : PRINT "Number of digits is"; digits PRINT "********************************": PRINT LOOP To verify for yourself, enter 2 when prompted for the base

80. New Scientist Breaking News - Largest Prime Number Ever Is Found It is only the 40th mersenne prime to have ever been found. Building blocks.mersenne primes were first discussed by Euclid in 350 BC and have been central http://www.newscientist.com/article.ns?id=dn4438

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