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  1. 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
  2. Illinois. University. Digital Computer Laboratory. Report by Donald Bruce Gillies, 1964
  3. Mersenne's numbers by Raymond Clare Archibald, 1935

21. Internet PrimeNet Server
PrimeNet is a distributed computing project for the Great Internet mersenne prime Search, coordinating the assignment of work and collection of results.
http://www.entropia.com/ips
2^p-1
Internet PrimeNet Server
Parallel Technology for the Great Internet Mersenne Prime Search Serious research. Totally for fun.
Join a search of mathematical discovery and become a part of Internet history. USD $100,000.00 Research Discovery Contest Free Participation Software News, Information

22. Ars Technica Team Prime Rib
A distributed computing team dedicated to finding mersenne prime numbers.
http://www.teamprimerib.com/

23. SS > Factoids > Mersenne Prime
home factoids mersenne prime. mersenne prime. A prime number of the formwhere p is prime. Each mersenne prime corresponds to an even perfect number.
http://www-users.cs.york.ac.uk/~susan/cyc/m/mersenne.htm
home factoids
Mersenne prime
A prime number of the form where p is prime.
  • The Mersenne number Mp is prime for exponent p For all other prime exponents less than Mp is composite, and for those less than 12,441,900 it is probably composite.
... it is the greatest that will ever be discovered for, as they are merely curious without being useful, it is not likely that any person will attempt to find one beyond it. Peter Barlow 1811, on M
  • Mersenne numbers have a particulary simple test for primality, the Lucas-Lehmer test The number-theoretic interest in Mersenne primes comes from the following theorem: if m and n are natural numbers, with n greater than 1, and if m n -1 is prime, then m is 2 and n is prime. Each Mersenne prime corresponds to an even perfect number The GREAT Internet Mersenne Prime Search help find another Mersenne prime! Chris Caldwell's Mersenne Primes Page history, lists, theorems, conjectures, ... Luke Welsh's Marin Mersenne Page biographies, prime number lists, algorithms, bibliography, ...

24. Mersenne Prime - Wikipedia, The Free Encyclopedia
mersenne prime. From Wikipedia, the free encyclopedia. In mathematics, a Mersenneprime is a prime number that is one less than a power of two.
http://en.wikipedia.org/wiki/Mersenne_prime
Mersenne prime
From Wikipedia, the free encyclopedia.
In mathematics , a Mersenne prime is a prime number that is one less than a power of two More generally, Mersenne numbers (not necessarily primes, but candidates for primes) are numbers that are one less than a prime power of two; hence,
M n n
Mersenne primes have a close connection to perfect numbers , which are numbers that are equal to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC Euclid demonstrated that if M is a Mersenne prime then M(M+1)/2 is a perfect number. Two millennia later, in the 18th century Euler proved that all even perfect numbers have this form. No odd perfect numbers are known, and it is suspected that none exist. It is currently unknown whether there is an infinite number of Mersenne primes. The calculation shows that M n can be prime only if n itself is prime, which simplifies the search for Mersenne primes considerably. But the converse is not true; M n may be composite even though n is prime. For example, 2

25. Great Internet Mersenne Prime Search - Wikipedia, The Free Encyclopedia
Great Internet mersenne prime Search. From Wikipedia, the free encyclopedia.The Great Internet claimed. mersenne primes found. Here is
http://en.wikipedia.org/wiki/Great_Internet_Mersenne_Prime_Search
Great Internet Mersenne Prime Search
From Wikipedia, the free encyclopedia.
The Great Internet Mersenne Prime Search , or GIMPS , is a collaborative project of volunteers, who use Prime 95 and MPrime , special open source software that can be downloaded from the Internet for free, in order to search for Mersenne prime numbers . The project was founded and the prime testing software was written by George Woltman Scott Kurowski wrote the PrimeNet server that supports the research to demonstrate Entropia distributed computing software, a company he founded in 1997. This project has been rather successful, although seemingly useless: it has found a total of 7 Mersenne primes , each of which was the largest known prime at the time of discovery. The largest known prime as of May , is 2 Josh Findley . Refer to the article on Mersenne primes numbers for the complete list of GIMPS successes As of March , GIMPS has a sustained throughput of approximately 14 teraflops Technically the GIMPS software is not open source , since it has a restriction which most open source/ free software EFF prizes are claimed.

26. GIMPS MERSENNE PRIME WORLD RECORD LARGEST FOUND BY GORDON SPENCE
Great Internet mersenne prime Search. and I found it !! Key Resource Links2 Go Key Resource Number Theory Topic. 36th mersenne prime Found.
http://www.rugeley.demon.co.uk/gimps/prime.htm
Great Internet Mersenne Prime Search
and I found it !!
Links Go Key Resource
Number Theory Topic
36th Mersenne Prime Found
On Sunday 24 th August 1997 I found the 36 th Mersenne Prime at the time it was the world's largest known prime number. It took my Pentium 100 PC fifteen days to prove the number prime. David Slowinski has verified the result on a Cray T90 Supercomputer. This new number is digits in length. George Woltman's announcement Chris Caldwell's announcement Read about it in Science News Article in the London Times ... CNN Article
How big is that ?
  • It would fill a 450 page paperback book If written out it would stretch for 1.4 miles or 2.2 Km It would take 28 days to say the number, speaking for 8 hours a day
Please note though that I was just the lucky one of over 4500 volunteers all searching for these gigantic numbers, why not join us......
.....GIMPS
Stands for the Great Internet Mersenne Prime Search, and is a world wide project involving over 4500 participants (@ September 1998), coordinated by George Woltman who maintains the GIMPS site and Scott Kurowski who runs the Primenet Internet Server . Every member of the group runs some Free Software Please note that this size of task would have previously only been possible on large Supercomputers such as the Cray that was used to verify this result, but by running the software on thousands of individual machines we can collectively surpass the power of even the most powerful supercomputer.

27. 40th Mersenne Prime Confirmed
here. 40th mersenne prime confirmed You count them in, you count themout again. By INQUIRER staff Tuesday 02 December 2003, 2148.
http://www.theinquirer.net/?article=12985

28. 40th Mersenne Prime Found
unsubscribe here. Advert. 40th mersenne prime found Needs verifyingyet. By INQUIRER staff Tuesday 18 November 2003, 1444. Tyan
http://www.theinquirer.net/?article=12732

29. New Scientist
student at Michigan State University used his office computer to contribute spareprocessing power to the Great Internet mersenne prime Search (GIMPS).
http://www.newscientist.com/news/news.jsp?id=ns99994438

30. Mersenne Prime
mersenne prime A Mersenne (also spelled Marsenne) prime is a specifictype of prime number. It must be reducible to the form 2 n
http://www.whatis.com/definition/0,,sid9_gci788348,00.html
Search our IT-specific encyclopedia for: or jump to a topic: Choose a topic... CIO CRM Databases Domino Enterprise Linux Exchange IBM S/390 IBM AS/400 Mobile Computing Networking Oracle SAP Security Storage Visual Basic Web Services Windows 2000 Advanced Search Browse alphabetically:
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B C D ... General Computing Terms Mersenne prime
A Mersenne (also spelled Marsenne) prime is a specific type of prime number . It must be reducible to the form 2 n - 1, where n is a prime number. The term comes from the surname of a French monk who first defined it. The first few known values of n that produce Mersenne primes are where n n n n n n n n n = 61, and n With the advent of computers to perform number-crunching tasks formerly done by humans, ever-larger Mersenne primes (and primes in general) have been found. The quest to find prime numbers is akin to other numerical searches done by computers. Examples are the decimal expansions of irrational number s such as pi (the circumference-to-diameter ratio of a circle) or e (the natural logarithm base). But the 'next' (unknown today, known tomorrow) prime is more difficult to find than the 'next' digit in the expansion of an irrational number. It takes the most powerful computer a long time to check a large number to determine if it is prime, and an even longer time to determine if it is a Mersenne prime. For this reason, Mersenne primes are of particular interest to developers of strong encryption methods.

31. Mersenne Prime
mersenne prime. A mersenne prime is a prime number that is one less than apower of two. mersenne prime Search home page http//www.mersenne.org.
http://www.fact-index.com/m/me/mersenne_prime.html
Main Page See live article Alphabetical index
Mersenne prime
A Mersenne prime is a prime number that is one less than a power of two Mersenne primes have a close connection to perfect numbers, which are numbers that are equal to the sum of their proper divisors. Historically, the study of Mersenne primes was motivated by this connection; in the 4th century BC Euclid demonstrated that if M is a Mersenne prime then M(M+1)/2 is a perfect number. Two millennia later, in the 18th century Euler proved that all even perfect numbers have this form. No odd perfect numbers are known, and it is suspected that none exist. It is currently unknown whether there is an infinite number of Mersenne primes. More generally, Mersenne numbers (not necessarily primes, but candidates for primes) are numbers that are one less than an odd power of two; the notation M n n shows that M n can be prime only if n itself is prime, which simplifies the search for Mersenne primes considerably. But the converse is not true; M n may be composite even though n is prime. For example, 2

32. The Top Twenty: Mersenne
MR 90c11009 See the conjectures in our page on mersenne primes. CW91 WN Colquittand Welsh, Jr., L., A new mersenne prime, Math. Comp., 56 (1991) 867870.
http://primes.utm.edu/top20/page.php?id=4

33. Mersenne Prime Numbers
mersenne prime Numbers. mersenne prime numbers are numbers of the form. Indeed, atpresent only 39 mersenne prime numbers are known. They are obtained by letting.
http://www.math.utah.edu/~alfeld/math/mersenne.html
Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah
Mersenne Prime Numbers
Mersenne prime numbers are numbers of the form For m to be prime, p itself must be prime, but that is not sufficient. Indeed, at present only 39 Mersenne prime numbers are known. They are obtained by letting p Note that for example so that for p = 11 we do not obtain a prime number. The largest prime number known is a Mersenne prime number. Mersenne prime numbers have their own web site which is dedicated to a netwide search for Mersenne prime numbers and related tasks. Fine print, your comments, more links, Peter Alfeld, PA1UM [06-Aug-1999]

34. 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.

35. Mersenne Prime Mailing List
mersenne prime Mailing List SignUp Sheet. One ongoing topic is thesearch for the next mersenne prime. The list is unmoderated.
http://www.ndatech.com/mersenne/signup.htm
Mersenne Prime Mailing List Sign-Up Sheet
The Mersenne Prime Mailing List was created to facilitate communication between those interested in all aspects of Mersenne Primes. One ongoing topic is the search for the next Mersenne Prime. The list is unmoderated. You can read all of the old posts in the list's older archives . You can also find some of the list's older digest archives and a recent searchable achive You are encouraged to read the FAQ before posting. This list is made possible by web pioneer Gordon Irlam who has generously configured his machine, base.com , to host the list. Thank you, gordoni! It is important to understand that there are THREE email addresses:
  • the list itself is mersenne @base.com, send messages to everybody
  • list maintenance is mersenne- request @base.com, ask to get on or off the list
  • list maintenance is mersenne-digest- request @base.com, ask to get on or off the magazine version
If you are having problems, there is a fourth address where you can ask the people running the list for help. Send email to:

36. Slashdot | (Mostly) Confirmed: New Mersenne Prime Found
(Mostly) Confirmed New mersenne prime Found. Science. until the 10 milliondigit mersenne prime is found, if one exists. very interesting
http://slashdot.org/science/01/11/14/1849203.shtml
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Hall of Fame ... Awards Services Broadband Online Books PriceGrabber Product News ... IT Research (Mostly) Confirmed: New Mersenne Prime Found Posted by Hemos on Wed Nov 14, '01 03:18 PM from the one-more-down-another-to-go dept. A reader writes "Distributed computing seems once more to be succesful. The combined effort of many pc's joining Primenet in search for a new Mersenne prime may have found there fifth result. Among them many belonging to /. readers. There is an unconfirmed claim for Mersenne prime #39 of over 3,500,000 digits, for which a considerable amount of money has been awarded SETI looks for ET's messages, but found none sofar. Mersenne primes are used to tell ET about us . A previous found Mersenne number was used to show the advance of science on our planet in a message send into outer space The Primenet list has confirmed that while they still need to totally test it out (which should be done by the 24th), they believe that the number found today is the 39th positive. Advertisement Slashdot Login Nickname: Password: Create a new account Related Links
  • Primenet Mersenne prime has been awarded SETI ... Also by Hemos
  • Science New Bacterium Could Herald Bio-Batteries The Year In Ideas Geminid Meteor Shower Linux Goes to Mars ... U.N. Delays Debate on Cloning

    37. Great Internet Mersenne Prime Search - Encyclopedia Article About Great Internet
    encyclopedia article about Great Internet mersenne prime Search. Great Internetmersenne prime Search. Word Word.
    http://encyclopedia.thefreedictionary.com/Great Internet Mersenne Prime Search
    Dictionaries: General Computing Medical Legal Encyclopedia
    Great Internet Mersenne Prime Search
    Word: Word Starts with Ends with Definition The Great Internet Mersenne Prime Search , or GIMPS , is a collaborative project of volunteers, who use Prime 95 is the name of the Windows-based software written by George Woltman that GIMPS, a distributed computing project researching Mersenne prime numbers, uses. There is also a Linux-based version named MPrime.
    See also
    • George Woltman
    • GIMPS
    • MPrime

    Click the link for more information. and MPrime MPrime is the name of the Linux and BSD software, written by George Woltman, that GIMPS, a distributed computing project researching Mersenne prime numbers, uses. It is entirely console based, with no requirement for X or any such thing. There is also a Windows-based version named Prime95.
    See also
    • George Woltman
    • GIMPS

    Click the link for more information. , special open source Open source open-source software."
    Click the link for more information. software Computer software (or simply software ) is the manifestation of a computer program in the form of data stored in the memory of a computer. This data can be

    38. Lucas-Lehmer Test For Mersenne Primes - Encyclopedia Article About Lucas-Lehmer
    encyclopedia article about LucasLehmer test for mersenne primes. for Mersenne numbers.A mersenne prime is a prime number that is one less than a power of two.
    http://encyclopedia.thefreedictionary.com/Lucas-Lehmer test for Mersenne primes
    Dictionaries: General Computing Medical Legal Encyclopedia
    Lucas-Lehmer test for Mersenne primes
    Word: Word Starts with Ends with Definition In mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships.
    Click the link for more information. , the Lucas-Lehmer test is a primality test A primality test is an algorithm for determining whether an input number is prime.
    Naive methods
    The simplest primality "test" is as follows: Given an input number N , we check each integer k > 1 other than N to see whether N is divisible by k . If so, then

    39. Math Lair - Mersenne Primes
    A lot of is currently being done by the Great Internet mersenne prime Search. Thelarger mersenne primes are the largest numbers which we know to be prime.
    http://www.stormloader.com/ajy/mersenne.html

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

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