81. Numbers: Glossary Whenever someone discovers a new Mersenne prime they also automatically discover a new perfect number. (2 1) x 2 is the world s largest known perfect http://www.richardphillips.org.uk/number/gl/prime.htm

Prime Numbers The first twelve prime numbers are - A number is called prime if its only factors are one and itself. Many numbers can be made by multiplying smaller numbers together. For example - 3 x 7 = 21 - 3 and 7 are called factors of 21. But some numbers cannot be made in this way and these are called prime numbers. For example, 23 is a prime number because it cannot be made by multiplying together smaller numbers. Numbers like 21 which are not prime are sometimes called composite numbers. All prime numbers, apart from 2, are odd numbers. The Mersenne primes are a special type of prime number. The first five are - - and they can be expressed as a power of two minus one - For a mathematician, the equivalent of breaking the 100 metres world record is to find the highest known prime number. Every year or so, someone discovers a higher one and it gets reported in the newspapers. These record-breaking numbers are always Mersenne primes. At the time of writing the highest known prime is 2 - 1. To write it out you would use 4,053946 digits and probably get through quite a few pencils. The record was broken in November 2001 by Michael Cameron using Prime 95 software by George Woltman.

82. Slashdot | (Mostly) Confirmed: New Mersenne Prime Found (Mostly) Confirmed New Mersenne Prime Found article related to Science. http://slashdot.org/science/01/11/14/1849203.shtml

83. News Blog: World Record ($100,000) Prime Number Found? Aug 28, 2008 Details are still sketchy but the Great Internet Mersenne Prime Search If it checks out, the finding of the 45th Mersenne prime (MP) http://www.scientificamerican.com/blog/post.cfm?id=world-record-100000-prime-num

84. Schneier On Security: 43rd Mersenne Prime Found Jan 23, 2006 Last month, researchers found the 43rd Mersenne Prime 2304024571. It s 9152052 decimal digits long. This is a great use of massively http://www.schneier.com/blog/archives/2006/01/43rd_mersenne_p.html

Bruce Schneier Blog Crypto-Gram Newsletter Books Essays and Op Eds ... Contact Information Schneier on Security A blog covering security and security technology. Main January 23, 2006 43rd Mersenne Prime Found Last month, researchers found the 43rd Mersenne Prime: 2 -1. It's 9,152,052 decimal digits long This is a great use of massively parallel computing The 700 campus computers are part of an international grid called PrimeNet, consisting of 70,000 networked computers in virtually every time zone of the world. PrimeNet organizes the parallel number crunching to create a virtual supercomputer running 24x7 at 18 trillion calculations per second, or 'teraflops.' This greatly accelerates the search. This prime, found in just 10 months, would have taken 4,500 years on a single PC. Posted on January 23, 2006 at 3:07 PM 36 Comments To receive these entries once a month by e-mail, sign up for the Crypto-Gram Newsletter Comments Not to discount the signifigance of this effort, but what's the use of finding these primes short of demonstrating human resourcefulness? Shouldn't we be using this processing power for folding proteins or the like? Posted by: Stephen at January 23, 2006 3:33 PM

85. Mersenne Prime Residues Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://comjnl.oxfordjournals.org/content/22/1/80.full.pdf

86. Aust. Math. Soc. Gazette Vol 24 No 4 by PG Brown Cited by 1 - Related articles http://www.austms.org.au/Gazette/1997/Nov97/brown.html

Australian Mathematical Society Web Site - the Gazette A NOTE ON RAMANUJAN'S CONJECTURES REGARDING `MERSENNE'S PRIMES' P. G. Brown In the so-called Lost Notebook of Ramanujan [1], pp. 259-260, Ramanujan says that when 2^p-1 is a prime, p may be termed a Mersenne's Prime. He then makes the following remarkable statements. a^2+ab+b^2 or of the form a^2+b^2 . Then since a number of the form cannot be expressed in any one of the above two forms, we infer that (2) A Mersenne's prime is never of the form . Thus for example a^2+ab+b^2 and the other containing primes that cannot be expressed as a^2+ab+b^2 (3) Hence the Mersenne's primes of the 1st-class except and are of the form , while those of the 2nd except are of the form (4) Theorem. If P be any prime, and p any odd prime and if either of or happens to be a prime, then that prime will be a Mersenne's prime of the 1st class. As a particular case we have when p = 3 (5) If P be any prime and if either of P^2+P+1 or happens to be a prime, then that prime will be a Mersenne's prime of the 1st class. (6) If p be a Mersenne's prime then 2^p-1 will be a Mersenne's prime of the 1st class. As examples of (5) and (6) we have

87. Math: I Can Never Remember — What Are All Of The Prime Numbers? - CliffsNotes A Mersenne prime is a prime number that is one less than a power of 2. One group calling themselves GIMPS (The Great Internet Mersenne Prime Search) http://www.cliffsnotes.com/Section/I-can-never-remember-what-are-all-of-the-prim

CliffsNotes - The Fastest Way to Learn My Cart My Account Help Home ... Management Math Sciences Test Prep Writing What's the best way to spend Halloween? Getting dressed up and going somewhere fun Taking kids trick or treating Staying home and watching scary TV Going to a haunted house or someplace really scary Ignoring the whole thing View Results Share This There are an infinite number of prime numbers; here are the first ten: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. A quick Internet search on list of prime numbers will turn up much longer lists. Some things to note: Notice that the number 1 is not prime; this is because a prime number must be divisible by two distinct numbers, and 1 is evenly divisible only by 1. Also, because all even numbers are divisible by 2, 2 is the only even prime number. All other prime numbers are odd. There is also a special set of prime numbers called Mersenne primes, named after French mathematician Marin Mersenne. A Mersenne prime is a prime number that is one less than a power of 2. For example, Because 31 is a prime number and 32 is a power of 2, 31 is a Mersenne prime. Mersenne primes are very rare, and no one knows for sure whether there are an infinite number of them. One group calling themselves GIMPS (The Great Internet Mersenne Prime Search) recently discovered the 44th Mersenne prime: 2

88. Ivars Peterson's MathTrek - Mersenne Megaprime Jul 26, 1999 The smallest Mersenne prime is 3 (22 1), or in binary digits, 11. After that comes 7 (23 - 1), or 111, then 31 (25 - 1), or 11111. http://www.maa.org/mathland/mathtrek_7_26_99.html

Ivars Peterson's MathTrek July 26, 1999 Mersenne Megaprime This time, it's a great leap forward. On June 1, a participant in the Great Internet Mersenne Prime Search (GIMPS) discovered the first known prime number with at least 2 million decimal digitsmore than twice as many as the previous record holder. The discoverer was Nayan Hajratwala, a consultant at PricewaterhouseCoopers in Plymouth, Mich. Using a Pentium-based personal computer and software written by George Woltman of Orlando, Fla., he identified 2 - 1 as a prime number, evenly divisible only by itself and 1. Its 2,098,960 decimal digits qualify Hajratwala for a $50,000 prize offered by the Electronic Frontier Foundation (EFF) in Palo Alto, Calif., for the first individual or group who discovers a prime number with at least 1 million digits. The newly discovered number is the 38th known Mersenne prime, named for the French cleric and mathematician Marin Mersenne (1588-1648). Expressed in the form 2 p - 1, where the exponent p is itself prime, Mersenne numbers have characteristics that make it relatively easy to determine whether a candidate is prime. For example, written out in binary form, a Mersenne number consists of an unbroken string of 1s6,972,593 of them in the case of the record holder. The smallest Mersenne prime is 3 (2 - 1), or in binary digits, 11. After that comes 7 (2

89. A NEW MERSENNE PRIME P 100000 [8, 10]. In Addition To These 28 Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.ams.org/mcom/1991-56-194/S0025-5718-1991-1068823-9/S0025-5718-1991-10

90. GIMPS - Great Internet Mersenne Prime Search's Journal I was wondering who else is on Live Journal and also helping with the Internet PrimeNet Server quest for the next Great Internet Mersenne Prime. http://community.livejournal.com/mersenneprimes

You are viewing the community mersenneprimes Log in Create a LiveJournal Account Learn more [Most Recent Entries] [Calendar View] [Friends] Below are the most recent journal entries recorded in GIMPS - Great Internet Mersenne Prime Search 's LiveJournal: Sunday, July 6th, 2008 2:17 am Anyone else both on LJ and questing for the next Great Internet Mersenne Prime? Hi! I was wondering who else is on Live Journal and also helping with the Internet PrimeNet Server quest for the next Great Internet Mersenne Prime. Presently, I'm: Rank Account ID LL P90* Exponents Fact.P90 Exponents P90 CPU CPU yrs LL Tested CPU yrs* w/ Factor hrs/day 1033. bmoshier 415.903 46 0.871 3 9081.94 P.S. I just realized I've been doing this for just a little over a year (started July 1, 2007 at 4:30 UTC). Current Mood: cheerful Current Music: Quietness 5 Comments Comment on this Thursday, November 9th, 2006 9:59 am mathemagician new gimps client p95v251 for those running windows, there is a new pre-beta client out that supports multithreading. I just happened to look at http://www.mersenne.org/gimps

91. Largest Known Prime Number On April 12, 2009, the 47th known Mersenne prime, 2242643801 1, a 12837064 digit number was found by Odd Magnar Strindmo from Melhus, Norway! http://www.pleacher.com/mp/mfacts/prime.html

Mersenne Prime Numbers On April 12, 2009, the 47th known Mersenne prime, 2 - 1, a 12,837,064 digit number was found by Odd Magnar Strindmo from Melhus, Norway! This prime is the second largest known prime number, a "mere" 141,125 digits smaller than the Mersenne prime found in August 2008. On September 6, 2008, the 46th known Mersenne prime, 2 - 1, a 11,185,272 digit number was found by Hans-Michael Elvenich in Langenfeld near Cologne, Germany! On August 23, 2008, Edson Smith using a UCLA computer discovered the 45th known Mersenne prime, 2 - 1, a mammoth 12,978,189 digit number! On September 4, 2006, Dr. Curtis Cooper and Dr. Steven Boone's CMSU team, found the largest known prime number at that time, 2 - 1. The prime number has 9,808,358 digits! This is the 44th Mersenne Prime Number. On December 15, 2005, Dr. Curtis Cooper and Dr. Steven Boone, professors at Central Missouri State University, discovered the 43rd Mersenne Prime, 2 - 1. The prime number has 9,152,052 digits!

92. Random Number Generators With Period Divisible By A Mersenne Prime File Format PDF/Adobe Acrobat Quick View http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.10.510&rep=rep1&

93. Leon Matthews | The Lost Continent Of Some really big prime numbers have been found by mathematicians over the years. The biggest prime found so far is a socalled Mersenne prime. http://lost.co.nz/numbers/primes.html

Skip over navigation I love deadlines. I love the whooshing sound they make as they fly by. Douglas Adams Home A Person Computing Library ... Websites Search this site Prime time That most indivisible of friends There's just something Um... right... but what is a prime number? Like jewels in... No, quite enough of that. A prime number is just a number that has no factors except itself and one. That is, it is not evenly divisible except by itself and the number one. This is most easily illustrated by example: 6 is divisible by 1, 2, 3 and itself. Not a prime. 13 is divisible only by one and itself. A prime! 64 is divisible by 1, 2, 4, 8, 16, 32, and itself. Definitely not a prime! By a strange coincidence 173, the street number of my current flat, and 347, the street number of my previous flat are also both prime numbers. Totally accidental, I promise. I'm sometimes a little odd, but not that much... As numbers get bigger, primes get rarer. Large primes have to 'resist' division from many more potential factors than do their lesser brethren. Despite that, primes keep popping up no matter how high up the integer food chain you go. Some really big prime numbers have been found by mathematicians over the years. The biggest prime found so far is a so-called Mersenne prime.

94. Numbers By George Hernandez Jump to Mersenne Prime Numbers The largest prime number known is a Mersenne prime number. Mersenne prime numbers have their own web site http://www.georgehernandez.com/h/xzMisc/Math/Numbers.asp

95. Grid Power: Sysadmin Discovers 13-million-digit Prime Number - Computerworld Sep 29, 2008 The discovery is part of the Great Internet Mersenne Prime Search (GIMPS), a 12 year-old project that uses the computers of volunteers to http://www.computerworld.com/s/article/9115799/Grid_power_Sysadmin_discovers_13_

96. Integers And Division File Format Microsoft Powerpoint View as HTML http://www.cs.virginia.edu/~asb/teaching/cs202-spring05/slides/11-integers-and-d

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