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         Mersenne Prime:     more detail
  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

81. From Warwick@mundook.cs.mu.OZ.AU (Warwick HARVEY) Newsgroups Sci
href= http//www.mersenne.org/prime.htm http//www.mersenne.org/prime.htm /a /a /a . It s the home page of The Great Internet mersenne prime Search (GIMPS
http://www.math.niu.edu/~rusin/known-math/97/mersens
From: warwick@mundook.cs.mu.OZ.AU (Warwick HARVEY) Newsgroups: sci.math.research Subject: Re: Mersenne Primes Date: 4 Dec 1997 08:09:52 GMT Brian D Koberlein

82. The Great Internet Mersenne Prime Search
The Great Internet mersenne prime Search. GIMPS, founded by prime. A Mersenneprime is a Mersenne number which is prime. Gimps connects
http://www.math-cs.cmsu.edu/~gimps/gimps.html
The Great Internet Mersenne Prime Search
GIMPS , founded by George Woltman in January of 1996, is dedicated to the rigorous search for new Mersenne primes. A Mersenne number is any number of the form 2 p - 1 where p is a prime. A Mersenne prime is a Mersenne number which is prime. Gimps connects the pure research of finding new Mersenne primes with the technology of the computer. The goal of GIMPS is to test the primality of every Mersenne number with an exponent less than 20,500,000. GIMPS uses a program written by Woltman that implements the Lucas-Lehmer Test and multiplies using Fast Fourier Transforms along with network software and the PrimeNet server developed by Scott Kurowski and the company Entropia . Over 12,000 number theory enthusiasts have harnessed thousands of small computers to search for these huge prime numbers using Woltman's program. GIMPS has now found the four largest known Mersenne primes. The following list gives these four Mersenne primes, their discoverer, and the date of their discovery.
-1 Joel Armengaud, George Woltman, GIMPS November 13, 1996

83. Mersenne Primes
numbers. A mersenne prime is always of the form 2 n 1 (n is a positiveinteger). For example,. 2 5 - 1 = 31 is a mersenne prime. Now
http://indigo.ie/~peter/prime.htm
New Largest Prime Numbers!

    Mersenne Primes Biologically, every male as an infant foetus initially enjoys a feminine identity. What may not be quite so obvious is that this parallels the very nature of the prime number system, which starts with an even (feminine) number. Indeed, this would suggest that every prime number can ultimately be derived from 2. A famous example of this approach is the set of Mersenne primes. (Another is the set of Fermat primes). Now Mersenne primes are especially interesting in that they also generate another fascinating class of numbers - with considerable psycho-mathematical significance i.e. perfect numbers. A Mersenne prime is always of the form 2 n - 1 (n is a positive integer). For example, - 1 = 31 is a Mersenne prime. Now, there are two points which I wish to point out which illustrate the transrational approach. 1) The power of 2 (i.e. the qualitative vertical number) must itself be prime, if the resulting number (i.e. the reduced quantitative horizontal number) is to be prime. In our example, the qualitative number 5 is prime, and the (reduced) quantitative number 31 is prime. 2) The resulting prime number is closely associated with a highly composite number.

84. RE: Mersenne: Prime

http://www.mail-archive.com/mersenne@base.com/msg06558.html
mersenne
Chronological Find Thread
RE: Mersenne: prime
  • From: Aaron Blosser
  • Subject: RE: Mersenne: prime
  • Date: Wed, 14 Nov 2001 22:52:46 -0800
mailto:mersenne-invalid- http://www.ndatech.com/mersenne/signup.htm http://www.tasam.com/~lrwiman/FAQ-mers http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ http://www.tasam.com/~lrwiman/FAQ-mers

85. RE: Mersenne: Prime

http://www.mail-archive.com/mersenne@base.com/msg06550.html
mersenne
Chronological Find Thread
RE: Mersenne: prime
  • From: George Woltman
  • Subject: RE: Mersenne: prime
  • Date: Wed, 14 Nov 2001 13:33:52 -0800
http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ http://www.tasam.com/~lrwiman/FAQ-mers

86. Mathematics Archives - Numbers
The Great Internet mersenne prime Search, Join over 6000 of your fellownumber theory enthusiasts in the search for new mersenne primes.
http://archives.math.utk.edu/subjects/numbers.html
Numbers
Facts about the number 17: 17 in history, computing, astronomy, etc. The 47 Society
The 47 Society is an international interest-group that follows the occurence and recurrence of the quintessential random number: 47. Many suspect that the coinciential nature of 47 carries some mystical, metaphysical and/or scientific significance.
What is special about the number 73939133? Aesthetics of the Prime Sequence
Hear and see the prime numbers! A Common Book of p The number p has been the subject of a great deal of mathematical (and popular) folklore. It's been worshipped, maligned, and misunderstood. Overestimated, underestimated, and legislated. Of interest to scholars, crackpots, and everyday people. Continued Fractions
A senior Honor's Project at Calvin College by Adam Van Tuyl which gives the history, theory, applications and bibliography on the thery of continued fractions. In the section on applications there are a number of interactive programs that convert rationals (or quadratic irrationals) into a simple continued fraction, as well as the converse. Data Powers of Ten A petabyte?

87. Number Theory --  Encyclopædia Britannica
Elementary number theory. Perfect numbers and mersenne primes. , Perfect numbersand mersenne primes from number theory The true origin of number theory is
http://www.britannica.com/eb/article?eu=117296&tocid=52279&query=number theory

88. Mersenne Primes
In 1995, the largest known was 2 1257787 1. Each mersenne prime gives rise toan even perfect number. Those that are prime are called mersenne primes.
http://www.bath.ac.uk/~ma2hlk/mersenne_prime.htm
Mersenne Primes Mersenne Primes: A prime of the form 2 p - 1, where p is a prime. The number of known primes of this form is over 30, and keeps increasing as they are discovered by using computers. In 1995, the largest known was 2 - 1. Each Mersenne prime gives rise to an even perfect number Marin Mersenne
Born: 1588
Died: 1648 Martin Mersenne was a french monk, philosopher and mathematician who provided a valuable channel of communication between such contempories as Descartes, Fermat, Galileo and Pascal: 'To inform Mersenne of a discovery is to publish it throughout the whole of Europe.' In an attempt to find a formula for prime numbers, he considered the numbers 2 p - 1, where p is a prime.
Not all such numbers are prime: 2 - 1 is not. Those that are prime are called Mersenne Primes. [Back to Prime Number page]
[Back to Number Theory page]

89. GIMPS (Great Internet Mersenne Prime Search)
GIMPS (Great Internet mersenne prime Search). GIMPS INFO. Using a largenumber of computers working together in a distributed computing
http://gilchrist.ca/jeff/distrib-gimps.html
GIMPS (Great Internet Mersenne Prime Search)
GIMPS INFO
Using a large number of computers working together in a distributed computing system, GIMPS is attempting to map all Mersenne primes starting from 0. If you are interesting in getting more information about GIMPS or would like to help by donating some idle CPU time, click here CURRENT GIMPS STATUS
CURRENT JEFF GILCHRIST STATUS Mersenne PrimeNet Server 4.0 (Build 4.0.031) Individual Account Report 03 Oct 1999 15:54 (Oct 3 1999 8:54AM Pacific) All dates and times are Coordinated Universal Time (UTC) Account ID LL P90* Exponents Fact.P90 Exponents P90 CPU CPU yrs LL Tested CPU yrs* w/ Factor hrs/day - - - - jeffg 2.172 16 0.006 26.88 Contact name : Jeff Gilchrist Contact e-mail : jeffg@cips.ca Receive e-mail : YES Last activity : 13 Aug 1999 15:17 UTC Account created: 23 Oct 1997 15:48 UTC *P90 CPU time according to Woltman/Kurowski formulation. Calibrated by benchmark P5 90Mhz, 32.98 MFLOP units: 25658999 FLOP/0.778s (256k FFT). (c)1997-1999 Entropia.com CURRENT JEFF GILCHRIST RANKING Mersenne PrimeNet Server 3.1 (Build 3.1.282) Top Producers Report 99-Jan-10 20:02 (Sun Jan 10 12:02 Pacific) This report is updated every 60 minutes Rank Account ID LL P90* Exponents Fact.P90 Exponents P90 CPU CPU yrs LL Tested CPU yrs* w/ Factor hrs/day - - - - - 1747. RobGreene 2.176 7 0.000 164.30 1748. S00877 2.173 13 1.791 55 57.97 1748. S05188 2.173 8 0.004 84.38

90. 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.

91. Definition Of Mersenne Prime - WordIQ Dictionary & Encyclopedia
mersenne prime. deMersennePrimzahl es A mersenne prime is a primenumber that is one less than a power of two. For example, 3 = 4
http://www.wordiq.com/definition/Mersenne_prime
Encyclopedia Dictionary Thesaurus The Web eBooks loadkeyword("Mersenne prime");
Mersenne prime
Encyclopedia Definition: Mersenne prime
da:Mersennetal de:Mersenne-Primzahl es:Número primo de Mersenne fr:Nombre premier de Mersenne ... nl:Mersenne priemgetal 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 an odd 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;

92. Javaguys Website - Help Calculate Mersenne Primes
Events, There are no upcoming events. Help calculate mersenne primes. GeneralNews For a long time, I ve been helping Calculate mersenne prime Numbers..
http://www.javaguy.org/geeklog/article.php?story=20030516102418705

93. CASNET List Archive: New Mersenne Prime Found
New mersenne prime found. The newest mersenne prime was found last week, as summarizedin a press release available at http//www.mersenne.org/2976221.htm.
http://www.casact.org/lists/casnet/00000039.htm
New Mersenne prime found
PHILBRS@tillinghast.com
Tue, 2 Sep 1997 12:43:56 -0400 I assume that some actuaries are interested in Mersenne Primes. If not,
my apologies for the interruption. The newest Mersenne Prime was found
last week, as summarized in a press release available at
http://www.mersenne.org/2976221.htm
The newest prime was found by a member of the GIMPS team (Great
Internet Mersenne Prime Search). I am a member of that team, and I have
two computers searching a range of possible values.
I note that the GIMPS team is made up of roughly 2000 volunteers.
Simple math tells me that if most casualty actuaries joined the team
(say 2000 of the 2500), then we would double the team size and the probability that the next prime would be found by an actuary would be roughly 1/2. (I realize that my numbers are optimistic, but a

94. CASNET List Archive: Re: New Mersenne Prime Found
Re New mersenne prime found. Next message Sce, Michael RE Simulation ;Maybe in reply to PHILBRS@tillinghast.com New mersenne prime found ;
http://www.casact.org/lists/casnet/00000043.htm
Re: New Mersenne prime found
kathy gile ( kgecorp@ix21.ix.netcom.com
Tue, 02 Sep 1997 21:30:09 -0500 PHILBRS@tillinghast.com wrote:
http://www.mersenne.org/2976221.htm
http://www.casact.org
Why not ALSO call on the SOA here? I know there are SOA members
interested in this.
BSG
Visit the CAS Web Site at http://www.casact.org
To subscribe or unsubscribe from CASNET:
Send an e-mail to caslists@lists.casact.org
Type in the body join casnet to subscribe or leave casnet to unsubscribe.

95. 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://home1.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.

96. GIMPS; The Great Internet Mersenne Prime Search
Metadata GIMPS; The Great Internet mersenne prime Search. Data Source SUB. Title,GIMPS; The Great Internet mersenne prime Search. Author, Woltman, George.
http://www.mathguide.de/cgi-bin/ssgfi/anzeige.pl/db=math/st=so1/ct=II
Metadata: GIMPS; The Great Internet Mersenne Prime Search
Data Source: SUB
BIBLIOGRAPHIC DATA Title GIMPS; The Great Internet Mersenne Prime Search Author Woltman, George Language English; Danish; French; Dutch; Italian; Polish Country (State) International Format of data text/html Keywords GIMPS; prime search; Mersenne; Mersenne prime; Mersenne numbers Description This page contains a description of the GIMPS Project. The goal is to test every Mersenne number with an exponent less than 5,260,000 by the year 2000. Also offered is a description of Mersenne numbers and some related links. URL http://www.mersenne.org/prime.htm Mirrored Dutch: http://www.dse.nl/~m31/mersenne/prime.htm; Italian: http://www.mclink.it/personal/MC5225/mersenne/prime-it.htm; Polish: http://www.polbox.com/g/gimps/ CLASSIFICATION Source Type Organizations and Societies MSCverbal Number theory MSC 11-XX ADDITIONAL INFORMATION Updated Access free Restrictions none Contents Clarity Index Links Level popular STATISTICS Server Statistics 151110 visitors since 19960801 Backlinks SSG-FI MathGuide Subject Source Type Local Search This document was created using Allegro V23

97. Mersenne Primes; History, Theorems And Lists
Metadata mersenne primes; History, Theorems and Lists. Data Source SUB. BIBLIOGRAPHICDATA. Title, mersenne primes; History, Theorems and Lists.
http://www.mathguide.de/cgi-bin/ssgfi/anzeige.pl?db=math&nr=000920&ew=SSGFI

98. Totse.com | The 32nd Mersenne Prime, Predicted By Mersenne
www.totse.com The 32nd mersenne prime, Predicted by Mersenne - The 32nd MersennePrime, Predicted by Mersenne. The 32nd mersenne prime, Predicted by Mersenne.
http://www.totse.com/en/technology/science_technology/32pri10.html
About Community Bad Ideas Drugs ... ABOUT
The 32nd Mersenne Prime, Predicted by Mersenne
The 32nd Mersenne Prime, FOUND by David Slowinski
Took 26.562767 minutes to calculate using
Maple 4.0 on a 512-MW 4 CPU Cray 2
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99. Citations Great Internet Mersenne Prime Search - Woltman
Retrieving documents G. Woltman, Great Internet mersenne prime Search, 1996. Home/Search Document Not in Database Summary Related Articles Check.
http://citeseer.ist.psu.edu/context/300857/0

100. New Mersenne Prime Found
New mersenne prime Found. For more information on this discovery and on Mersenneprimes, check out the MAA Online at (http//www.MAA.org/news/mersenne.html).
http://www.math.ncsu.edu/undergrad/Newsletter/v3.3/art02.html
New Mersenne Prime Found
Prev Contents Next
Gordon Spence, using the GIMPS (Great Internet Mersenne Prime Search) program (written by George Woltruan) and a Pentium machine, recently discovered that
is prime
This number has almost 900,000 digits and is now the largest known prime number. For more information on this discovery and on Mersenne primes, check out the MAA Online at ( http://www.MAA.org/news/mersenne.html

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