81. Hardwareluxx: Downloads/CPU Sharing/Mersenne Prime Translate this page Suche nach im gesamten Katalog nur in dieser Kategorie, erweiterteSuche. Home Downloads CPU Sharing mersenne prime. LINKS http://www.hardwareluxx.de/pages/Downloads/CPU_Sharing/Mersenne_Prime/

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82. Mersenne Primes A mersenne prime is a prime number of the form 2 p 1, where p is a prime. The currentrecord-holding mersenne prime garnered a $50,000 prize from the EFF. http://www.jcu.edu/math/vignettes/mersenne.htm

Vignette 19 Mersenne Primes A prime number is an integer greater than 1 whose only positive divisors are 1 and the number itself. Thus, the numbers 2, 3, 5, 7, 11, 13, 17, ... are prime. In Vignette 2 , you saw an elementary proof that there are infinitely many prime numbers. It was also pointed out that there is no formula that will generate all primes in sequence. Because of this fact, both professional and amateur mathematicians have for years attempted to determine larger and larger prime numbers. Mersenne Primes Since no formula can generate all prime numbers, attention has turned to looking for prime numbers that have a specific form. One such form that has been explored a great deal is that of Mersenne primes , named for Marin Mersenne, a French monk who began the study of these numbers in the early 1600's. A Mersenne prime is a prime number of the form 2 p - 1, where p is a prime. For instance, 2 - 1= 3 is prime, 2 - 1 = 7 is prime, 2 - 1 = 31 is prime, and so on. Not all such numbers are prime, however; for example, 2 89 is not prime.

83. Trailpost 2 Properties Of Prime Numbers A special type of prime is called a mersenne prime. For example, the number 7is a mersenne prime since 2 3 1 = 8 - 1 = 7 and 7 is a prime number. http://www.cs.usask.ca/resources/tutorials/csconcepts/numbertheory/tutorial/trai

84. Home.earthlink.net/~neilbawd/gimp2001.txt \ ****New mersenne prime December 5, 2001 http://home.earthlink.net/~neilbawd/gimp2001.txt

85. The Great Internet Mersenne Prime Search - The Perl Journal, Winter 1997 The Great Internet mersenne prime Search. David Nicol. Until I computingdevices. Since 127 is prime, Lucas' prime is also a mersenne prime. 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.

86. ONJava.com: Web Services And The Search For Really Big Prime Numbers [Aug. 29, 2 Such as? This article shows how Web services are an ideal model for computingmersenne prime numbers, some of the largest primes yet discovered. http://www.onjava.com/pub/a/onjava/2002/08/28/wsdc.html

Newsletters Events Jobs API Map ... O'Reilly's Emerging Technology Conference: April 22-25, 2003 Topics J2EE/CORBA JSP and Servlets EJB Components JDO/JDBC/SQLJ ... Java SysAdmin Content Feature Articles Java API Map Web Logs Book Excerpts ... Newsletters Stay informed. Subscribe to our weekly ONJava newsletter. Java Jobs To learn about the hottest Java jobs, click here Resources Open For Business Dec. 19, 2002 jTans Dec. 16, 2002 ICESoft Java Browser and Web Application Client Dec. 13, 2002 JPublish Dec. 13, 2002 Millstone Dec. 11, 2002 Books Mac OS X for Java Geeks Java Data Objects Java Extreme Programming Cookbook JDBC Pocket Reference ... Learning Java, 2nd Edition Affiliates Servlets.com jdom.org Print Email article link Web Services and the Search for Really Big Prime Numbers by Eoin Lane What do searching for extraterrestrials, curing cancer, and finding big prime numbers all have in common? These problems are all being attacked with grid computing, a a technique of breaking a large problem into small tasks that can be computed independently. While projects like Seti@home and The Greatest Internet Mersenne Prime Search have received plenty of press for using the Internet to distribute tasks to end users around the globe, grid computing also takes place in more controlled environments, such as research and financial settings. But it is by using the power of the Internet and the ability to discover and access idle processes on users' machines that grid computing (once called

87. GIMPS The Great Internet mersenne prime Search. Back to The Dicken Expresshome page. Last updated 6/10/01. GIMPS Whereas some people doodle http://pages.prodigy.net/rjdicken/gimps.htm

The Great Internet Mersenne Prime Search Back to The Dicken Express home page Last updated 6/10/01. Whereas some people doodle and others daydream, one of my eccentricities has been to pass the time during dull lectures or other long waits making lists of prime numbers or trying to figure out if a number, say 1,327, is prime. (Yes, it is.) So I was intrigued to learn about the Great Internet Mersenne Prime Search where a simple program can be downloaded to a home computer to determine whether massively large numbers of a special type are prime. (For fellow geeks, Mersenne numbers , named after the 17th century French monk Marin Mersenne , are in the form of 2 to the exponent p (a prime number) minus 1, i.e. 2 p -1.) In fact, this project has found the 4 largest known prime numbers . The largest known prime number, 2 -1, was discovered by a GIMPS participant on June 1, 1999 and is 2,098,960 digits long! Now, when my home computer (a Pentium-III 650 Mhz) is not being used to surf the web, balance our checkbook, or play JumpStart First Grade, it is quietly churning out repetition after repetition of a formula to determine if an over 1-million digit number is prime. Anyone who finds the 39th known Mersenne prime against odds of greater than 50,000 to 1 for each number currently being tested will have found the largest known prime number of any kind. If the next prime has over 10-million digits, a $100,000 award is available! Even if a number proves not to be prime, it will still contribute to the efforts of several thousand other PC users to systematically eliminate Mersenne numbers as not prime. If you would like to join, too

88. Numcom09 Before we define what a mersenne prime is, we need to explain the meaning of thesymbol ^ in expressions such as 2^3 (read 2 to the power of 3) for the benefit 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.

89. Mathematics Enrichment Workshop: The Perfect Number Journey If a Mersenne number turns out to be a prime number, then it is calleda mersenne prime. (c) Do you think M 21 is a mersenne prime? http://home.pacific.net.sg/~novelway/MEW2/lesson2.html

How are Mersenne primes related to perfect numbers? If a Mersenne number turns out to be a prime number, then it is called a Mersenne prime You have computed the first 5 Mersenne primes: 3, 7, 31, 127, 8191. Each of these numbers in turn gives a perfect number when multiplied by its previous power of 2. Just to summarise what we have done so far, let's examine Table 2 again. This time, we will express the numbers in powers of two, and delete those rows that do not carry perfect numbers. Exercise 4 (a) Complete the following table, expressing the first five Mersenne primes and perfect numbers in powers of two. Table 4: The first five Mersenne primes and the corresponding perfect numbers. (b) Two perfect numbers were discovered in 1588, both by Cataldi. These two perfect numbers can be obtained from the Mersenne primes M - 1 and M - 1. Can you compute these two perfect numbers with the help of your calculator? (c) Do you think M is a Mersenne prime? By now, you should have realised why numbers of the form 2 n - 1 have so much appeal. Whenever a prime number of this form is found, a perfect number is immediately obtained, as was proven by Euclid.

90. Biography Of Marin Mersenne Whenever another mersenne prime is found, another perfect number isgenerated. GIMPS stands for Great Internet mersenne prime Search. http://www.andrews.edu/~calkins/math/biograph/199899/biomerse.htm

Back to the Table of Contents Marin Mersenne His Life Marin Mersenne was a 17th century monk and mathematician, who mainly studied the numbers 2 p Marin Mersenne is best known for his role as a sort of clearing house for correspondence between eminent philosophers and scientists, and for his work in number theory. Mersenne's Accomplishments Many early writers felt that the numbers of the form 2 p - 1 were prime for all primes p, but in 1536 Hudalricus Regius showed that 2 - 1 = 2047 was not prime. By 1603 Pietro Cataldi had correctly verified that 2 - 1 and 2 - 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 Mersenne. Marin Mersenne investigated prime numbers and he tried to find a formula that would represent all prime numbers. Although he failed in this, his work on the numbers 2

91. Temple University News Bureau - Top Stories His targets are rare, incredibly large numbers known as mersenne prime numbers,and his weapon is a collection of nearly 300 computers in the Educational http://www.temple.edu/news_media/td844.html

LARGE NUMBERS IN PRIME TIME AT TEMPLE UNIVERSITY AS COMPUTERS PURSUE MATHEMATICAL PREY AT RECORD PACE Marc Getty , the network administrator for Temple University's College of Liberal Arts, is hunting prey. His targets are rare, incredibly large numbers known as Mersenne prime numbers, and his weapon is a collection of nearly 300 computers in the Educational Technology Center (ETC) of Temple's College of Liberal Arts. Among prime numberswhole positive numbers evenly divisible by only themselves and 1there is a special subset, Mersenne primes, which take the form 2p - 1, in which p is prime. In centuries of scholarship, mathematicians have been able to find and confirm only 37 Mersenne primes. Perhaps due to their scarcity, these numbers have given rise to the Great Internet Mersenne Prime Search (GIMPS), an international computer-based effort by researchers and math buffs to find more of them. Leading the way is Temple, where hundreds of machines in the ETC have churned out a record number of checksall of them negativeof potential Mersenne primes. Getty is spearheading the University's involvement with GIMPS. According to him, the project has practical applications in the fields of computer encryption, national security, and general mathematical scholarship.

92. 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://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.

93. What Is A Mersenne Prime? What is a mersenne prime? keywords=math, formula, algorithm Mersenne's When2^n1 is prime it is said to be a mersenne prime. Testing http://mediagods.com/glossary/What_is_a_Mersenne_prime.html

mediagods glossary Glossary How-To's ... Suggest What is a Mersenne prime? keywords=math, formula, algorithm Mersenne's Conjecture states that 2 raised to a power minus 1 is a prime. When 2^n-1 is prime it is said to be a Mersenne prime. Testing new primes is very computation intensive and is currently a popular application for distributed computing projects. News for Mar 18, 2003 The Macintosh News Network DeltaGraph 5.0 for Mac OS... Apps: JJEdit, PhotoCaster... Apple Power Supply Exchan... PB Developer Note ... Iomega adds 256MB Iomega ... Slashdot Dissecting Localized Goog... A Photorealistic CGI TV S... Linux.Com Linux Advisory Watch - Ma... The U.S. as a second-clas... OSXFAQ OSXFAQ - New and Updated ... OSXFAQ - Mac OS X Unix Ti... OSXFAQ - Mac OS X Tip-of-... PlaybackTime Apple to introduce Mac-on... When only the very worst ... Still seeking contributin... Webmonkey PHP4 Installation Overview SMIL: Multimedia for the ... Forms, Files, and ASP Streaming For Dollars ... MediaGods Privacy Statement

94. Mersenne Primer mersenne primer. What is a mersenne prime? They are known as Mersennenumbers, and only called mersenne primes if they are prime. http://www.sheeplechasers.org/prime/mersenne.htm

Mersenne Primer What is a Mersenne prime? A Mersenne prime is a prime number (a number divisible only by itself and 1) of the form 2^n-1; for instance, 7 = 2^3-1. They are named for Marin Mersenne , who investigated prime numbers, especially of this form. Not all numbers of the form 2^n-1 are prime; actually they are quite rare. For starters, for 2^n-1 to be prime, 'n' must be prime. For this reason you will usually see the form written as 2^p-1, where 'p' is a prime number. Even so, most numbers of the form 2^p-1 are still not prime. They are known as Mersenne numbers, and only called Mersenne primes if they are prime. Both are sometimes represented as 'Mp'. Mersenne primes and perfect numbers A perfect number is a number that is equal to the sum of its factors, provided you count '1' as a factor but not the number itself. Why is that? I don't know, you'd have to ask the ancient Greeks. Probably because if you don't use that definition then there are no perfect numbers. Now it just so happens that all known perfect numbers are of the form (2^p-1)*2^(p-1). The first two are 6 (=1+2+3) and 28 (=1+2+4+7+14). They are given by the formula for p = 2 and p = 3. You may have noticed that the first half of that formula is the form of a Mersenne prime. It also holds true that the number given by the formula will not be a perfect number unless 2^p-1 is prime. There's a good reason for that. Let's look again at that perfect number formula. It's always a Mersenne number times a power of 2. Let's let n = p-1, so that can be rewritten as "Mp * 2^n". The factors of 2^n are [1, 2, 4, 8,... 2^(n-1), 2^(n)], which add up to 2^(n+1)-1. So the factors of our alleged perfect number (Mp*2^n) will contain those powers of 2, plus Mp, plus Mp times powers of 2 up to 2^(n-1). (We can't count Mp times 2^n because that is the number itself.) Now the sum of Mp times powers of two from 1 to 2^(n-1) is Mp*(2^n-1).

95. A Large Prime Number As of February 11, 1998, the Largest Known Primes web site lists a recordholder of 3021377 2 1 which is a mersenne prime of 909,526 digits. http://www.cs.arizona.edu/icon/oddsends/bigprime.htm

A Large Prime Number As of February 11, 1998, the Largest Known Primes web site lists a record holder of which is a Mersenne prime of 909,526 digits. You can download its digits At that time, the largest recorded non- Mersenne prime was which has only 91,241 digits, making it small enough to list here: Icon home page

96. VACETS Technical Column - Tc48 The new prime number, 2^12577871 (which denotes 2 multiplied by itself 1,257,787times minus one) is the 34th mersenne prime, discovered by David Slowinski http://www.vacets.org/tc/tc48.html

VACETS Regular Technical Column The VACETS Technical Column is contributed by various members , especially those of the VACETS Technical Affairs Committe. Articles are posted regulary on vacets@peak.org forum. Please send questions, comments and suggestions to vacets-ta@vacets.org September 10, 1996 Largest Known Prime Number Discovered About 2 years ago, Andrew Wiles, a researcher at Princeton, claims to have proved the Fermat's Last Theorem (FLT) and later a large gap was found in the proof. (The gap was filled later at the end of 1994.) At that time, we, the VACETSERS, had debated on proving the FLT using numerical methods (i.e., using computer to crank out the solutions to the famous theorem). One of the first steps in numerical method is to find the prime numbers, and from that, a "fastest prime number generator" war was waged among us the VACETSERS. The result of that "war" was that we were able to reduce the time from tens of seconds to find all the primes below 1 million to less than 1 second to find all the primes below 10 million. It was an improvement of more than 100. It was a fun war. (Actually, for me, anything involved with numbers, especially prime numbers, is fun.) Shortly after that "fastest prime number generator" war, Thomas R. Nicely, Professor of Mathematics at Lynchburg College, Virginia, computed the sums of the reciprocals of the twin primes (such as 11 and 13), triplets (such as 11, 13, and 17), and quadruplets (such as 11, 13, 17, and 19) up to a very large upper bound (about 10 trillion). He discovered during the summer and fall of 1994 that one of the reciprocals had been calculated incorrectly by a Pentium computer, although a 486 system gave the correct answer; this led to the publicization of the hardware divide flaw in the Pentium floating point unit.

97. Number Nabbers Bag Biggest Prime Clarkson's discovery is the 37th known mersenne prime. Welsh was thecodiscoverer of the 29th mersenne prime, 2 110503 - 1, in 1988. http://www.unc.edu/depts/cmse/math/Mersenne.html

CMSE Online Front Page ProgramGuide courses and workshops NewsLink math/science education news Sitefinder access to teaching resources FeatureIndex browse our past features SiteIndex complete table of contents Number Nabbers Bag Biggest Prime On June 1, 1999, an ordinary Pentium PC in Plymouth, Michigan, found the largest known prime number, a number having 2,098,960 digits (enough to fill a 1000-page paperback book). The newly discovered prime replaces the previous record-holder, a number having 909,526 digits. The champion computer belongs to Nayan Hajratwala, who works for Price Waterhouse Coopers in Plymouth, Michigan. The old record (set in January 1998) belonged to Roland Clarkson, a 19-year-old student at California State University. Mr. Hajratwala and Mr. Clarkson are participating in a unique international project to find new primesand anyone who wishes to do so can join this effort. An anonymous donor posted a $50,000 prize for the first million-digit prime; Mr. Hajratwala will be eligible for this award as soon as the discovery is published by a recognized mathematial journal. There's a $100,000 prize offered for the first ten-million-digit prime. Prime numbers are whole numbers having no proper divisors, that is, a number p is prime if its only divisors are 1 and p itself. The first ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. Mathematicians can easily prove that there exist infinitely many primes, but it is very difficult to determine whether a given large number is prime or not.

98. Prime Numbers Historical topics about prime numbers.Category Science Math Number Theory Prime Numbers...... The largest known prime (found by GIMPS Great Internet mersenne prime Searchin December 2001) is the 39th mersenne prime M 13466917 which has 4053946 http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html

99. :: G I M P S . I T :: Homepage Del Team_Italia 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

Benvenuti sul sito GIMPS.IT Ricerca dei numeri primi di Mersenne by This site has moved to GIMPS.IT

100. :: G I M P S . I T :: Homepage Del Team_Italia Translate this page Benvenuti sul sito GIMPS.IT. Ricerca dei numeri primi di mersenne.by Team_Italia. This site has moved to GIMPS.IT! http://www.mclink.it/personal/MC5225/mersenne/prime-it.htm

Benvenuti sul sito GIMPS.IT Ricerca dei numeri primi di Mersenne by This site has moved to GIMPS.IT

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