81. Thraxil / Keyword / Mersenne Prime mersenne prime. nodes; Distributed Computing and Prime Numbers by Miguel Diaz. http://thraxil.org/keywords/mersenne-prime/

@import "/css/thraxil_unsafe.css"; mersenne prime nodes Distributed Computing and Prime Numbers by Miguel Diaz

82. GIMPS At Albany These three things come together in the Great Internet mersenne prime Search, Well, no, we haven t actually found a mersenne prime yet what Lennart http://hawk.fab2.albany.edu/mersenne/mersenne.htm

Mersenne Meets Minerva GIMPS at the University at Albany Since late August 1997, more than 80 PCs on faculty, staff, and student desktops and in instructional labs have become part of an experiment at Albany in distributed massively parallel processing (DMPP) if you accept 85 as "massive." If not, please check back. We're continually adding more machines. There is a three-fold purpose to this project. Firstly, we want to show that there are many idle PC cycles that can be used productively in a networked environment. Even if your screen is strewn with icons and open windows, even if you occasionally have two or three or eight Web searches going at once, even if you feel frantically busy trying to get several tasks completed, that's your sense of busy. The reality is that your processor is usually on vacation. On call, of course, but nonetheless on vacation. If you are running NT workstation on your PC, open Task Manager and click on the "Processes" tab. You will find that "System Idle" only rarely drops below 90%! That is not an argument against upgrading PCs, which is necessary in order to take advantage of 32-bit buses, large memory, huge disks, faster video cards, and everything else that new applications increasingly expect. Rather it is an argument for identifying, capturing, and using those idle cycles even if you are not the one who uses them. But that's another story.

83. Prime Numbers By 2005 a total of 42 mersenne primes have been found. The largest knownprime (found by GIMPS Great Internet mersenne prime Search in February 2005) http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html

Prime numbers Number theory index History Topics Index Version for printing Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras 's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers. A perfect number is one whose proper divisors sum to the number itself. e.g. The number 6 has proper divisors 1, 2 and 3 and 1 + 2 + 3 = 6, 28 has divisors 1, 2, 4, 7 and 14 and 1 + 2 + 4 + 7 + 14 = 28. A pair of amicable numbers is a pair like 220 and 284 such that the proper divisors of one number sum to the other and vice versa. You can see more about these numbers in the History topics article Perfect numbers By the time Euclid 's Elements appeared in about 300 BC, several important results about primes had been proved. In Book IX of the Elements Euclid proves that there are infinitely many prime numbers. This is one of the first proofs known which uses the method of contradiction to establish a result. Euclid also gives a proof of the Fundamental Theorem of Arithmetic: Every integer can be written as a product of primes in an essentially unique way.

84. Slashdot | 42nd Mersenne Prime Probably Discovered 42nd mersenne prime Probably Discovered article related to Education and Science. http://science.slashdot.org/article.pl?sid=05/02/18/1855206&tid=146&tid=14

85. Perfect Numbers And Mersenne Primes Perfect numbers and mersenne primes. A prime number of the form $ 2^p1$ iscalled a mersenne prime. As we ve seen already, it is unknown whether or not http://web.usna.navy.mil/~wdj/book/node19.html

Next: Primality testing Up: Primes Previous: The Fundamental Theorem of Contents Index Perfect numbers and Mersenne primes It is remarkable that even at this ``elementary'' level there are many problems which are still unsolved. In this section, we mention one of the oldest unsolved problems in mathematics. Let be an integer and let For example, Definition 1.5.12 A perfect number is an integer such that , in other words, is the sum of its proper divisors. No odd perfect numbers are known. The following conjuecture may be the oldest unsolved problem in mathematics! Conjecture 1.5.13 Odd perfect numbers don't exist. It is known if an odd perfect number exists then it must be at least Lemma 1.5.14 An integer is an even perfect number if and only if , where is a prime. Though this result is often quoted as being due to Euler, it may have been known to Euclid. proof : We leave the ``if'' direction as an exercise. ``Only if'': Since is an even number, we can write , where is odd and . We know that , so let , with . Since , we have: which gives us: Therefore

86. 39th Mersenne Prime Discovered Announcing the discovery of the 39th mersenne prime. http://www.lehigh.edu/~bad0/13466917bd.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 first 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!" "Finding this prime is by far our most impressive accomplishment to date, having taken two years of non-stop work. In addition to congratulating Michael Cameron, we wish to thank all 130,000 volunteer home users, students, schools, universities and businesses from around the world that contributed to GIMPS," said GIMPS founder George Woltman. "Joining GIMPS is a great way to learn about math through participation - plus you might find a new Mersenne prime, like Michael."

87. The Great Internet Mersenne Prime Search The Great Internet mersenne prime Search Paper by Patrick Kellogg. http://www.patrickkellogg.com/school/papers/gimps.htm

Return to the home page for Patrick Kellogg The Great Internet Mersenne Prime Search The “Great Internet Mersenne Prime Search” is a large distributed computing project sponsored by the Mersenne organization at: http://www.mersenne.org/prime.htm . It was started by George Woltman in 1994 to find Mersenne primes, and in the last six years the group has found the four largest ones currently known. In addition to GIMPS, they also sponsor several other distribute mathematical projects at (http://www.mersenne.org/). Why would anyone want to try to find the next Mersenne prime? Well, besides the altruistic idea of contributing to scientific knowledge, the Electronic Frontier Foundation ( www.eff.org ) is offering a $100,000 reward to the first person that helps to discover a ten million digit (or higher) prime number. There are some caveats $25,000 goes to charity and $20,000 to GIMPS, but it still leaves $55,000 for the lucky computer user. And the 1 in 250,000 odds are better than most state lotteries. Installation of the GIMPS software is easy. Different versions are available for Microsoft Windows 95/98 and NT/2000 (as well as the earlier 3.1), Linux, FreeBSD, OS/2 and DOS. Also, optimized code is available for different platforms, including PowerPC, StrongARM, UNIX, and older x86 machines. Though the software does not support multiple processors or multiple machines working on the same problem, they have a very robust server at “PrimeNet” (

88. The 32nd Mersenne Prime By David Slowinski - Project Gutenberg Start here to download the Project Gutenberg eBook of The 32nd mersenne prime byDavid Slowinski. http://www.gutenberg.org/etext/69

Project Gutenberg Online Book Catalog Quick Search Author: Title Word(s): EText-No.: Advanced Search Recent Books Top 100 Offline Catalogs ... In Depth Information The 32nd Mersenne Prime by David Slowinski Read online Help on this page New Search Bibliographic Record Creator Slowinski, David Title The 32nd Mersenne Prime Predicted by Mersenne Note Math Language English LoC Class QA: Science: Mathematics Subject Numbers, Prime Subject Number theory EText-No. Release Date No Formats Available For Download Edition Format Encoding ¹ Compression Size Download Links ² Plain text none 241 KB main site mirror sites Plain text zip 121 KB main site mirror sites ¹ If you need a special character set, try our online recoding service ² If you are located outside the U.S. you may want to download from a mirror site located near you to improve performance. Click on mirror sites to select a mirror site. If you have P2P software installed that understands magnetlinks click on Most recently updated: 2005-09-13 09:46:15

89. Mathenomicon.net : News : 40th Mersenne Prime Disovered The Great Internet mersenne prime search announces the discovery of a new Mersenneprime. http://www.cenius.net/news/news.php?ArticleID=10

90. Mathenomicon.net : News : New Mersenne Prime Found GIMPS has announced the discovery of the 41st known mersenne prime. http://www.cenius.net/news/news.php?ArticleID=13

91. Historia Matematica Mailing List Archive: Re: [HM] New Mersenne Prime! press release about the NEW mersenne prime will be posted athttp//www.mersenne.org/prime.htm quite shortly. And, as a matter of fact,navigators (surfers? http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jul99/0017.html

Re: [HM] New Mersenne Prime! Julio Gonzalez Cabillon jgc@chasque.apc.org Sun, 04 Jul 1999 23:10:06 -0300 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Samuel S. Kutler: "[HM] New Perfect Number" Previous message: Gregory Moore: "[HM] Geometry and Sets" In reply to: Alfred Ross: "[HM] The Arabic Version of Euclid's Optics" Dear Colleagues, A few hours ago, George Woltman kindly informed me that the official press release about the NEW Mersenne prime will be posted at http://www.mersenne.org/prime.htm quite shortly. And, as a matter of fact, navigators (surfers?) right now can read online this prime information at http://www.mersenne.org/6972593.htm Great Internet Mersenne Prime Search (GIMPS) Finds First Million-Digit Prime, Stakes Claim to $50,000 EFF Award. 2^6,972,593 - 1 is now the Largest Known Prime. "ORLANDO, Florida, June 30, 1999 Nayan Hajratwala, a participant in the Great Internet Mersenne Prime Search (GIMPS), has discovered the first known million-digit prime number using software written by George Woltman and the distributed computing technology and services of Scott Kurowski's company, Entropia.com, Inc. The prime number

92. Historia Matematica Mailing List Archive: [HM] New Mersenne Prime! The last entry in the Chris Caldwell s Table of Known mersenne primes at 2^69725931 seems to be the new mersenne prime, although http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jul99/0001.html

[HM] New Mersenne Prime! Antreas P. Hatzipolakis xpolakis@otenet.gr Thu, 1 Jul 1999 21:53:08 +0300 (EET DST) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Ivan Van Laningham: "Re: [HM] Kosnita" Previous message: Antreas P. Hatzipolakis: "Re: [HM] Kosnita" The last entry in the Chris Caldwell's Table of Known Mersenne Primes at: http://www.utm.edu/research/primes/mersenne.shtml reads: 6xxxxxx ~2000000 ~4000000 1999 Woltman, Kurowski et. al. (GIMPS, PrimeNet) Richard Schroeppel informed us (in the math-fun list; see below) that p = 6972593 Antreas FWD Message Date: Thu, 1 Jul 1999 11:08:40 -0700 (MST) rcs@cheltenham.CS.Arizona.EDU To: math-fun@cheltenham.CS.Arizona.EDU Subject: 2^6972593-1 2^6972593-1 seems to be the new Mersenne prime, although I haven't seen the "official" word. There are lots of smaller not-yet-checked exponents. Rich rcs@cs.arizona.edu END - Next message: Ivan Van Laningham: "Re: [HM] Kosnita" Previous message: Antreas P. Hatzipolakis: "Re: [HM] Kosnita"

93. The Great Internet Mersenne Prime Search - The Perl Journal, Winter 1997 Since 127 is prime, Lucas prime is also a mersenne prime. Currently 35 Mersennenumbers are known to be prime, and more are being tested even as you are http://www.foo.be/docs/tpj/issues/vol2_4/tpj0204-0012.html

PREVIOUS TABLE OF CONTENTS NEXT The Great Internet Mersenne Prime Search David Nicol Until I became acquainted with GIMPS, the Great Internet Mersenne Prime Search (http://www.mersenne.org), the idle cycles on my workstation were spent entirely in wait states. No longer. Now my computer continuously runs a program that breaks new mathematical ground. Even as I write this, it's running in the intervals between my keystrokes, factoring large numbers as part of an Internet-wide coordinated effort to find the highest known prime number. In this article I'll describe how I use Perl not for factoring - a C program does that - but for automating communication with the computer (and person) in charge of GIMPS. Recently, the world has seen two large problems successfully attacked with massively distributed systems, an approach sometimes called "metacomputing." On June 18, the DES Challenge (DESCHALL), which teamed up computers around the world to decipher a message encrypted with a 56-bit RSA secret key, succeeded. On August 24, the GIMPS project demonstrated that 2 -1 is a prime number. Both DESCHALL and GIMPS are computer programs that ran with low priority on thousands of computers volunteered around the world.

94. Load Of Tosh : GIMPS Finds 40th Known Mersenne Prime GIMPS finds 40th known mersenne prime. From www.mersenne.org On November 17,2003 Michael Shafer s computer found the 40th known mersenne prime, http://blogs.msdn.com/tmeston/archive/2003/12/02/40814.aspx

load of tosh a web mail developer RSS 2.0 Atom 0.3 Blog Home Contact ... Nov December 2003 Jan S M T W T F S Search Go Archives June 2005 (3) February 2005 (1) January 2005 (2) December 2004 (9) ... June 2003 (15) News My name is Tosh Meston. I am a Microsoft developer working on the Outlook Web Access team. Navigation Home Blogs Post Categories .NET (rss) Blogging (rss) ... (rss) People I am reading Kristen Meston .NET Weblogs Eric Sink: The Business of Software Blogs.MSDN.com ... KC Lemson MSDN A Fond Farewell All Work and No Play Standard Answers Redmond's Gray Skies of Summer ... Coming Up for Air Sports InfiniteHoops.com InfiniteSoccer.com InfiniteSoftball.com Life Online Orkut Profile Photoblog / Moblog MSN Space Featured Sites BabyPhotoBlog.com posted on Tuesday, December 02, 2003 4:31 PM by Tosh Meston GIMPS finds 40th known Mersenne Prime From www.mersenne.org On November 17, 2003 Michael Shafer's computer found the 40th known Mersenne prime, 2 -1! This number "weighs in" at a whopping 6,320,430 decimal digits! This is also the largest known prime number, surpassing GIMPS' last discovery by over 2 million digits. Here's the number in case you are interested.

95. Load Of Tosh : Four Years Of Mersenne Prime Searching Four Years of mersenne prime Searching. Hmmm it s been four years of runningGIMPS (Great Internet mersenne prime Search) software on my machines and in http://blogs.msdn.com/tmeston/archive/2003/07/19/10286.aspx

load of tosh a web mail developer RSS 2.0 Atom 0.3 Blog Home Contact ... Jun July 2003 Aug S M T W T F S Search Go Archives June 2005 (3) February 2005 (1) January 2005 (2) December 2004 (9) ... June 2003 (15) News My name is Tosh Meston. I am a Microsoft developer working on the Outlook Web Access team. Navigation Home Blogs Post Categories .NET (rss) Blogging (rss) ... (rss) People I am reading Kristen Meston .NET Weblogs Eric Sink: The Business of Software Blogs.MSDN.com ... KC Lemson MSDN A Fond Farewell All Work and No Play Standard Answers Redmond's Gray Skies of Summer ... Coming Up for Air Sports InfiniteHoops.com InfiniteSoccer.com InfiniteSoftball.com Life Online Orkut Profile Photoblog / Moblog MSN Space Featured Sites BabyPhotoBlog.com posted on Saturday, July 19, 2003 12:36 AM by Tosh Meston Four Years of Mersenne Prime Searching Hmmm...  it's been four years of running GIMPS (Great Internet Mersenne Prime Search) software on my machines and in that time I've checked 117 exponents and the project has found 2 Mersenne prime numbers (prime numbers of the form 2 ^P I still think projects like these are a good use of spare cycles.  What distributed computing software do you run?

96. Mersenne Prime Numbers Such prime numbers are called nowa-days mersenne primes and p is called its (prime)exponent. A table ordered by discovery date follows http://wwwhomes.uni-bielefeld.de/achim/mersenne.html

For which positive integers p is p a prime number? Such prime numbers are called now-a-days Mersenne Primes and p is called its (prime) exponent. A table ordered by discovery date follows: Rank exponent p discovery date discoverer (credited persons) needed time to prove supporting help Pietro Cataldi Pietro Cataldi Leonhard Euler Francois Edouard A. Lucas I. M. Pervushin R. E. Powers R. E. Powers Raphael M. Robinson ~ 80 sec SWAC Raphael M. Robinson ~ 2 min SWAC Raphael M. Robinson 13.5 min SWAC Raphael M. Robinson ~ 55 min SWAC Raphael M. Robinson 1 hour SWAC Hans Riesel 5.5 hours BESK ~ 50 min IBM 7090 50 min IBM 7090 Donald B. Gillies 83 min ILLIAC II Donald B. Gillies 90 min ILLIAC II Donald B. Gillies 135 min ILLIAC II Bryant Tuckerman 35 min IBM 360/91 CDC Cyber 174 CDC Cyber 174 Cray 1 David Slowinski Cray 1 David Slowinski Cray X-MP David Slowinski Cray X-MP/24 686 sec NEC SX/2 ~ 16 hours Cray-2 7.2 hours Cray C90 ~ 6 hours Cray T90 Joel Armengaud, Woltman, et. al. 88 hours 90 MHz Pentium PC Gordon Spence, Woltman, et. al. 15 days 100 MHz Pentium PC Roland Clarkson, Woltman, Kurowski et. al.

97. Entropia Grid Powers Mersenne Project's Discovery Of Largest Known Prime Number The new mersenne prime, expressed as 2 to the 13466917th power minus 1, It belongs to a special class of rare prime numbers called mersenne primes. http://www.hoise.com/primeur/02/articles/monthly/AE-PR-01-02-34.html

Entropia Grid powers Mersenne Project's discovery of largest known prime number San Diego 11 December 2001 Entropia and Mersenne.org announced that Michael Cameron, a 20 year-old participant in the worldwide mathematics research project called the Great Internet Mersenne Prime Search (GIMPS), has discovered the largest known prime number using his PC connected to the Entropia Mersenne Grid. Entropia and Mersenne.org run GIMPS jointly. Entropia created the distributed computing technology and maintains the global Grid that harnesses spare CPU cycles to accelerate the discovery of these rare numbers. Mersenne.org developed the application software that runs on this Grid and performs the calculations to discover these prime numbers. GIMPS has 130,000 volunteer participants with more than 210,000 PCs. The new Mersenne prime, expressed as 2 to the 13,466,917th power minus 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 first studied the numbers. Mersenne primes are most relevant to number theory and have practical implications for encryption and computational benchmarking. GIMPS started running on the Entropia Grid in 1997, making it one of the first Internet Grid projects available for public participation. Ernst Mayer, Paul Victor Novarese, and Guillermo Ballester Valor each independently verified the new number using server hardware and number crunching software combinations each different from the other. The discovery is the fifth record prime found by the GIMPS project, and the third discovered using Entropia's Grid for distributed computing. Previous Mersenne primes discovered by GIMPS participants have been recognised as the world's largest in

98. Mersenne Project Discovers Largest Known Prime Number On Worldwide Volunteer Com and belongs to a special class of rare prime numbers called mersenne primes .The discovery marks only the 40th known mersenne prime, named after Marin http://www.hoise.com/primeur/04/articles/monthly/AE-PR-01-04-37.html

EnterTheGrid - Primeur Monthly EnterTheGrid - Primeur is the premier Grid and Supercomputing information source in the world. With Primeur Monthly we provide you a free update with news and in-depth stories. Primeur Magazine PrimeurLive! EnterTheGrid Analysis ... Contact Primeur Monthly - issue January 2004 Industry HPCN industry ENACTS - a Cooperation Network in EC's "Improving Human Potential - Access to research Infrastructures Programme" Reader's comments on machine evaluation workshop report ... Cornell Theory Center offers course in Windows-based clusters Mersenne Project discovers largest known prime number on worldwide volunteer computer Grid Orlando 02 December 2003 Michael Shafer, a 26 year-old volunteer in the Mersenne.org research project called the Great Internet Mersenne Prime Search (GIMPS), has discovered the largest known prime number. Michael Shafer used a Michigan State University lab PC and free software by George Woltman and Scott Kurowski as part of an international Grid of 211,000 networked computers in virtually every time zone of the world. Advertisement Advertisement The new number, expressed as 2 to the 20,996,011th power minus 1, has 6,320,430 decimal digits and was discovered November 17th. It is more than two million digits larger than the previous largest known prime number, and belongs to a special class of rare prime numbers called Mersenne primes . The discovery marks only the 40th known Mersenne prime, named after Marin Mersenne , a 17th century French monk who first studied the numbers 300 years ago.

99. New Largest Prime Discovered! This new largest prime, 2259649511, is only the 42nd known mersenne prime, You can buy a framed or unframed poster of this mersenne prime, http://plus.maths.org/latestnews/jan-apr05/mersenne42/

about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Latest news Spaghetti breakthrough What happens to bent pasta? How to measure a million The risks in Who wants to be a millionaire? Not just knots: the secrets of khipu The Inka way of counting Machine prose A computer program that can learn languages A new time machine Take a journey to the limits of common sense Gene-ius The search for the maths gene Plus... more news from the world of maths Explore the news archive Subscribe to our free newsletter Get the ... posters! News New largest prime discovered! Image www.freeimages.co.uk The largest known prime has just been discovered, not by a university academic, but by a German eye surgeon, Dr Martin Nowak , thanks to his participation in the Great Internet Mersenne Prime Search (GIMPS). The bad news is that his discovery has made him no money - he was a mere 2,183,770 digits off a share of a $100,000 prize. But the good news is that anyone with some computer power to spare could unearth the next big prime, and even win some cold hard cash. This new largest prime, 2

100. About "Mersenne Prime Freeware" mersenne prime Freeware. _ Library Home Full Table of Contents Suggest a Link Library Help http://mathforum.org/library/more_info.html?id=6192

Page 5     81-100 of 116    Back | 1  | 2  | 3  | 4  | 5  | 6  | Next 20