101. #226232 - ITP: Glucas -- Mersenne Prime Testing Program - Debian Bug Report Logs New mersenne prime FoundGordon Spence, using the GIMPS (Great Internet mersenne prime Search) program (writtenby George Woltruan) and a Pentium machine, recently discovered that http://bugs.debian.org/226232

Debian Bug report logs - ITP: glucas Mersenne prime testing program Package: wnpp ; Maintainer for wnpp is wnpp@debian.org Reported by: ; Date: Mon, 5 Jan 2004 09:48:05 UTC. Severity: wishlist; Done: damog@cerdita.damog.net (David Moreno Garza). View this report as an mbox folder Report forwarded to debian-bugs-dist@lists.debian.org, debian-devel@lists.debian.org, wnpp@debian.org Bug#226232 ; Package wnpp Full text and rfc822 format available. Acknowledgement sent to New Bug report received and forwarded. Copy sent to debian-devel@lists.debian.org, wnpp@debian.org Full text and rfc822 format available. Message received at submit@bugs.debian.org ( full text mbox From: To: submit@bugs.debian.org Subject: ITP: glucas Mersenne prime testing program Date: Sun, 4 Jan 2004 21:05:25 -0800 http://glucas.sourceforge.net/ License : GPL v2 Description : Mersenne prime testing program Glucas tests Mersenne numbers (2^P-1) for primality using the Lucas-Lehmer method. It can be used to participate in the Great Internet Mersenne Prime Search ( http://www.mersenne.org

102. GRIDtoday: GIMPS PROJECT DISCOVERS NEW LARGEST KNOWN PRIME NUMBER The discovery marks only the 41st known mersenne prime, named after Previous GIMPS mersenne prime discoveries were made by members in various countries. http://www.gridtoday.com/04/0621/103394.html

DAILY NEWS AND INFORMATION FOR THE GLOBAL GRID COMMUNITY / ( Previous Article ) ( Table of Contents ) Special Features: GIMPS PROJECT DISCOVERS NEW LARGEST KNOWN PRIME NUMBER Josh Findley, a volunteer in the Mersenne.org research project called the Great Internet Mersenne Prime Search (GIMPS), has discovered the largest known prime number. Findley used his home PC and free software by George Woltman and Scott Kurowski as part of an international Grid of 240,000 networked computers in virtually every time zone of the world. The new number, expressed as 2 to the 24,036,583th power minus 1, has 7,235,733 decimal digits and was discovered May 15. It is nearly a million digits larger than the previous largest known prime number, and belongs to a special class of rare prime numbers called Mersenne primes. The discovery marks only the 41st known Mersenne prime, named after Marin Mersenne, a 17th century French monk who first studied the rare numbers 300 years ago. Mersenne primes are most relevant to number theory, but most participants join GIMPS simply for the fun of having a role in real research and the chance of finding a new Mersenne prime. GIMPS is closing in on the $100,000 Electronic Frontier Foundation award for the first 10-million-digit prime. The new prime is 72 percent of the size needed. However, "an award-winning prime could be mere weeks or as much as few years away that's the fun of math discoveries," said GIMPS founder George Woltman.

103. Mersenne Primes Mersenne Numbers Primes. In the statements below p is an odd prime. All 2p1have the form 8k+7 They also have the form pk+1, This is from the Little http://home.earthlink.net/~usondermann/mer.html

In the statements below p is an odd prime. All p have the form They also have the form pk+1, This is from the Little Fermat Theorem where p is mod p therefore by adding 1 to both sides we get p is 1 mod p. This may be a clue to the factors of p that are composite. My guess is that pk+1 is a factor, k p p Here is a look at the Mersenne Composites Another obvious fact is that (p-1) is mod p, E.G. has a factor of Here is a another tidbit If p is prime then p is divisible by can be factored into p p since is also factorable by because the exponent is composite since p is prime and factors to p p or must divide p Here is a look at some Fermat Numbers Last updated: 5/26/98 Webmaster: Ulrich (Ulie) Sondermann usondermann@earthlink.net

104. BoothNet : 117 Mersenne Primes 117 mersenne primes. The results of who found which prime can be found on themarks page, where they re given in terms of the index of the prime found. http://www.ma.umist.ac.uk/rb/teaching/117/mersenne.html

Booth Net Teaching Mersenne Primes 117 Mersenne Primes The results of who found which prime can be found on the marks page , where they're given in terms of the index of the prime found. To save you recalculating them, here's a slightly different list; the first 22 Mersenne primes. I'll insert a space every 60 characters, to avoid stretching our browser windows too wide. Enjoy! Rank n 2^n-1 teaching research contact rfbooth.com ... R.F.Booth . Opinions may not be those of anyone. Want to talk about it This page was last modified on October 6, 2001.

105. [rc5] Mersenne Primes, What Good Are They? rc5 mersenne primes, what good are they? Ryan Dumperth woodie at indy.net WedOct 1 024338 EDT 1997. Previous message rc5 messerene primes http://lists.distributed.net/pipermail/rc5/1997-October/033034.html

106. VMUNIX Blues » New Mersenne Prime! The news is also covered in depth at The Great Internet mersenne prime Searchsite the distributed software that found the new prime. http://www.vmunix.com/mark/blog/archives/2003/12/03/new-mersenne-prime/

VMUNIX Blues Home New Mersenne Prime! December 3rd, 2003 New Scientist The news is also covered in depth at The Great Internet Mersenne Prime Search Download the program and help out! Entry Filed under: General Leave a Comment Name Required Email Required, hidden Url Comment Some HTML allowed: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <code> <em> <i> <strike> <strong> Subscribe to the comments via RSS Feed Calendar December 2003 M T W T F S S Most Recent Posts Flickr Slowness New Sun Galaxy Servers Build Your Own Router One more thing... ... Blix Theme by Sebastian Schmieg. Icons by Kevin Potts . Powered by WordPress Login

107. ARIA - GIMPS Project There are only 39 mersenne primes known, and the GIMPS project has The 40thmersenne prime might have been found 17th Nov 2003, see GIMPS page. http://www.aria.uklinux.net/mersenne.php

Mersenne Primes - GIMPS Project Main Homepage Articles Printer Friendly Pages Software NURBS Toolbox Tips and Tricks Misc Mersenne Primes GIMPS , the Great Internet Mersenne Prime Search, was formed in January 1996 to discover new world-record-size Mersenne primes. GIMPS harnesses the power of thousands of small computers to search for primes of the form 2 P There are only 39 Mersenne primes known, and the GIMPS project has discovered five Mersenne primes so far. The 40th Mersenne Prime might have been found 17th Nov 2003, see GIMPS page. Confirmation will be early December. Date Name P 17th Nov 2003 14th Nov 2001 Michael Cameron 1st June 1999 Nayan Hajratwala 27th Jan 1998 Roland Clarkson 24th Aug 1997 Gordon Spence Nov 1996 Joel Armengaud The table below show the progress up the GIMPS ranks. Rank LL P90* Exponents Fact.P90 CPU yrs LL Tested CPU yrs* dmspink@aria.uklinux.net

108. The Lost Continent Of - That's Our Last Contact With Civilisation What s a mersenne prime? Marin Mersenne Glad you asked. mersenne primes are asmall subset of ordinary prime numbers that happen to take a special form — a http://www.lost.co.nz/main/numbers/primes.html

home a person computing library ... World Pop. Clock 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.

109. Mersenne Primtal Søgningen En koordineret søgning efter Mersenne primtal. GIMPS er forkortelsen for detengelske navn Great Internet mersenne prime Search . http://www.infohome.dk/mersenne/

i Danmark GIMPS GIMPS hjemmesider på engelsk fransk hollandsk italiensk ... spansk og tysk Ialt 17.550 deltagere verden over! Seneste programversion Seneste Prime95-version: . Hent den her Status Se din egen GIMPS status her Placering Se din samlede placering her GIMPS Nyheder her Primenet FAQ her Mersenne FAQ her GIMPS Hjemmesiden "Moder"-hjemmesiden for GIMPS findes her Hvad er GIMPS GIMPS er forkortelsen for det engelske navn: "Great Internet Mersenne Prime Search". Konkret går det ud på at bruge den CPU-tid, din pc alligevel ikke bruger til at afvikle andre programmer, mens du arbejder, til at finde nye primtal. Så synes du det er synd, at der går CPU-tid til spilde på din pc, når den alligevel står og kører, så kan du være med til at bruge den gratis tid til noget godt. Nytter det noget? Hvordan virker det? Bruger du Windows 95, Windows 98, Windows ME, Windows NT eller Windows 2000 skal du bare hente programmet her Hvad nu hvis jeg bruger noget andet? her , eller finde source-koden til programmet her Hvad er Mersenne tal?

110. Mathematica And Mersenne Primes mersenne primes have long played an important role in number theoryfor Though mersenne primes have been studied for centuries, many fundamental http://www.wolfram.com/products/mathematica/usersanduses/experience/mersenne.htm

PreloadImages('/common/images2003/btn_products_over.gif','/common/images2003/btn_purchasing_over.gif','/common/images2003/btn_services_over.gif','/common/images2003/btn_new_over.gif','/common/images2003/btn_company_over.gif','/common/images2003/btn_webresource_over.gif'); Products Mathematica What is Mathematica ... Give us feedback Sign up for our newsletter: Mathematica and Mersenne Primes In June 1999 an international group of mathematicians, computer scientists, and hobbyists, who had joined under the banner of the Great Internet Mersenne Prime Search (GIMPS), discovered that 2 -1 is prime. The number is currently the largest known prime. The discoverers are officially listed as N. Hajratwala, G. Woltman, and S. Kurowski, the first person being the volunteer whose machine actually found the prime and the latter persons being the software/network architects. This prime is 2,098,960 decimal digits long and therefore qualifies for a $50,000 prize from the Electronic Frontier Foundation . One interesting sidelight is that in the early 1990s Mathematica played an important part in making the discovery possible.

111. Great Internet Mersenne Prime Search - Rechenkraft Mersenne-Primzahlen. Kommerziell,nein. Homepage, www.mersenne.org/prime.htm http://217.160.138.71/wiki/index.php?title=Great_Internet_Mersenne_Prime_Search

112. Prime Numbers Directory A compilation of links related to prime numbers including primality tests, lists of prime numbers, factoring, mersenne numbers and the Goldbach conjecture. http://cochise.mta.ac.il:8080/~liorb/servlet/Categories

113. Ricerca Dei Numeri Primi Di Mersenne 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

G.I.M.P.S. Home Page Febbraio 2005: Nuovo numero Primo di Mersenne Pagine disponibili in Danese Olandese Francese Tedesco ... Polacco e Spagnolo . Attenzione: Alcune traduzioni potrebbero non essere aggiornate - usare AltaVista se necessario. Trovato il 42mo numero primo di Mersenne! Il 18 Febbraio 2005, il Dr. Martin Nowak dalla Germania, ha trovato il nuovo numero primo più grande: 2 -1. Il numero primo ha 7,816,230 cifre ! Sono stati necessaripiù di 50 giorni di calcolo sul Pentium 4 2,4 GHZ del Dr. Nowak. Il nuovo numero primo è stato verificato indipendentemente in 5 giorni da Tony Reix di Grenoble, Francia, utilizzando un computer Bull NovaScale 5000 HPC con 16 CPU Itanium attraverso il programma Glucas scritto da Guillermo Ballester Valor di Granada, Spagna. Il Dr. Martin Nowak, un chirurgo degli occhi residente in Michelfeld, Germany è venuto a conoscenza del GIMPS nell'Aprile del 1999, quando lesse un articolo sul suo giornale locale, il "Frankfurter Allgemeine Zeitung" . Il Dr. Nowak, un matematico dilettante, ha iniziato con un PC e con il crescere delle sue capacità crebbe il suo interesse e la sua partecipazione nel GIMPS. Sei anni dopo, egli si ritrova con 24 computer dedicati al lavoro di calcolo per il GIMPS ed un numero primo di Mersenne al suo attivo! Perfectly Scientific , la ditta del Dr. Crandall che ha sviluppato l'algoritmo FFT utilizzato dal GIMPS, ha a disposizione un

114. [Prime] RE: New Mersenne ? prime RE New mersenne ? Greg Edwards gedwards at sgi.com Thu May 5 051031PDT 2005. Previous message prime New mersenne? Next message prime RE http://hogranch.com/pipermail/prime/2005-May/000684.html

[Prime] RE: New Mersenne ? Greg Edwards gedwards at sgi.com Thu May 5 05:10:31 PDT 2005 Previous message: [Prime] New Mersenne? Next message: [Prime] RE: New Mersenne ? Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] I'm not sure, but I may be guilty here. I reverified M127 just to prove it works (I mean 2**127 -1) I didn't expect an already tested number would be included in the stats. If so, we can easily ? frivolously ? valuably disguise the next real Mersenne Prime. Greg E -Original Message- From: prime-bounces at hogranch.com [mailto: prime-bounces at hogranch.com ] On Behalf Of prime-request at hogranch.com Sent: Thursday, 5 May 2005 5:00 AM To: prime at hogranch.com Subject: Prime Digest, Vol 13, Issue 3 Send Prime mailing list submissions to prime at hogranch.com To subscribe or unsubscribe via the World Wide Web, visit http://hogranch.com/mailman/listinfo/prime or, via email, send a message with subject or body 'help' to prime-request at hogranch.com You can reach the person managing the list at prime-owner at hogranch.com

115. Ricerca Dei Numeri Primi Di Mersenne Translate this page Una ricerca organizzata dei numeri primi di mersenne. Comprende software gratuito. http://www.mclink.it/personal/MC5225/mersenne/prime-it.htm

G.I.M.P.S. Home Page Febbraio 2005: Nuovo numero Primo di Mersenne Pagine disponibili in Danese Olandese Francese Tedesco ... Polacco e Spagnolo . Attenzione: Alcune traduzioni potrebbero non essere aggiornate - usare AltaVista se necessario. Trovato il 42mo numero primo di Mersenne! Il 18 Febbraio 2005, il Dr. Martin Nowak dalla Germania, ha trovato il nuovo numero primo più grande: 2 -1. Il numero primo ha 7,816,230 cifre ! Sono stati necessaripiù di 50 giorni di calcolo sul Pentium 4 2,4 GHZ del Dr. Nowak. Il nuovo numero primo è stato verificato indipendentemente in 5 giorni da Tony Reix di Grenoble, Francia, utilizzando un computer Bull NovaScale 5000 HPC con 16 CPU Itanium attraverso il programma Glucas scritto da Guillermo Ballester Valor di Granada, Spagna. Il Dr. Martin Nowak, un chirurgo degli occhi residente in Michelfeld, Germany è venuto a conoscenza del GIMPS nell'Aprile del 1999, quando lesse un articolo sul suo giornale locale, il "Frankfurter Allgemeine Zeitung" . Il Dr. Nowak, un matematico dilettante, ha iniziato con un PC e con il crescere delle sue capacità crebbe il suo interesse e la sua partecipazione nel GIMPS. Sei anni dopo, egli si ritrova con 24 computer dedicati al lavoro di calcolo per il GIMPS ed un numero primo di Mersenne al suo attivo! Perfectly Scientific , la ditta del Dr. Crandall che ha sviluppato l'algoritmo FFT utilizzato dal GIMPS, ha a disposizione un

116. Henri LIFCHITZ's Mersenne And Fermat Primes Field Henri Lifchitz's single general form contains the main remarkable numbers of number theory. http://ourworld.compuserve.com/homepages/hlifchitz/Henri/us/MersFermus.htm

Mersenne and Fermat primes field Let NMF(b,p,n)= (b^ (p^(n+1)) -1)/(b^ (p^n) These numbers contain under the single general form the main remarkable numbers of number theory.Indeed, we obtains : - for b=2 and n=0 those are Mersenne's numbers - for b=+/-2 et p=2 those are Fermat's numbers - for b even and p=2 those are Generalized Fermat repunits base b. These numbers can be considered as Generalized Mersenne , they can be prime only if p is prime. rep.base-1 . These numbers can also be considered as Generalized Mersenne , with the same property for p. - for p=3 we obtain numbers of the form (b 3^n -1)b 3^n which we can name Generalized Mersenne-Fermat in particular for the combined form of their divisors n+1 A general form of the divisors of these numbers will be noted of more : n+1 . We find again 2kp+1 for Mersenne's numbers and k2 n+2 +1 for Fermat's numbers. For n=1 and p=m not necessarily prime we find also (b m +/-1)b m (see New forms of primes ), but the form of the divisors is more complex generally. The table below summarizes the organization and the specificities of these numbers : Divisors Generalized M ersenne (rep. base-1)

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