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Mersenne Prime:     more books (16)

The 32nd Mersenne Prime - Predicted by Mersenne by David Slowinski, 2010-07-06 Calcul Distribué: Great Internet Mersenne Prime Search, Cluster Beowulf, Grille Informatique, Calcul Parasitaire, Seti@home (French Edition) Great Internet Mersenne Prime Search Classes of Prime Numbers: Twin Prime, Mersenne Prime, Fermat Number, Sophie Germain Prime, List of Prime Numbers, Wieferich Prime Some notes on multiplicative congruential random number generators with Mersenne prime modulus [2.sup.61]-1.: An article from: Journal of the South Carolina Academy of Science by James Harris, 2003-09-22 Integer Sequences: Prime Number, Factorial, Binomial Coefficient, Perfect Number, Carmichael Number, Integer Sequence, Mersenne Prime Nombre Premier de Mersenne: Great Internet Mersenne Prime Search, Nombre Parfait, 7, 3, 31, Mersenne Twister, 2305843009213693951, 127 (French Edition) The 32nd Mersenne Prime, FOUND by Math Books, 2008-05-29 Prime Numbers: Prime Number, Prime Number Theorem, Ulam Spiral, Great Internet Mersenne Prime Search Perfect Numbers: Perfect Number, Mersenne Prime, 6, 28, List of Perfect Numbers, 496 Marin Mersenne: An entry from Gale's <i>Science and Its Times</i> by Judson Knight, 2001 Three new Mersenne primes, and a conjecture (Illinois. University. Digital Computer Laboratory. Report) by Donald Bruce Gillies, 1964 The 32nd Mersenne Prime Predicted by Mersenne The 32nd Mersenne Prime Predicted by Mersenne

lists with details

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
    
    Extractions: - 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 - 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
    
    Extractions: Bruce Schneier Blog Crypto-Gram Newsletter Books Essays and Op Eds ... Contact Information A blog covering security and security technology. Main 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 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
    
    Extractions: Australian Mathematical Society Web Site - the Gazette 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
    
    Extractions: 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
    
    Extractions: Ivars Peterson's MathTrek July 26, 1999 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

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

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
    
    Extractions: I love the whooshing sound they make as they fly by. Douglas Adams That most indivisible of friends There's just something 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: 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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