41. Mathenomicon.net : Reference : Mersenne Prime A External link to http//wwwhistory.mcs.st-andrews.ac.uk/Mathematicians/Mersenne.htmlmersenne prime is a Mersenne number (a natural number of the form http://www.cenius.net/refer/display.php?ArticleID=mersenneprime

42. ThinkQuest : Library : Distributed Computing Huge prime numbers are the bounty of the Great Internet mersenne primeSearch. Great Internet mersenne prime Search. page 1 2. Fig. http://library.thinkquest.org/C007645/english/2-mersenne-0.htm

Index Hardware Distributed Computing Our website focuses on how distributed computing helps with research in scientific and technical fields. Its inexpensive cost and computing power is drawn from thousands of users across the Internet. It also looks at computer networks, distributed computing on a smaller scale, and how the real world uses them, from service delivery networks to library terminals. Visit Site 2000 ThinkQuest Internet Challenge Languages French Spanish Students Lindsey Redlands East Valley HS, Mentone, CA, United States Steven Redlands East Valley HS, Loma Linda, CA, United States Coaches Vince Redlands East Valley HS, Mountain View, CA, United States jim Redlands East Valley HS, Redlands, CA, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

43. Great Internet Mersenne Prime Search GIMPS Great Internet mersenne prime Search. What is a mersenne prime? mersenne primesare those primes who have the notation 2 p -1 where p is a prime number. http://www.geocities.com/CapeCanaveral/Launchpad/4403/gimps.html

GIMPS- Great Internet Mersenne Prime Search GIMPS- The Great Internet Mersenne Prime is an organization of over 6000+ people donating their computer's CPU time toward find Mersenne Primes. To join, you must download a program called Prime95 (about 323K (900K unzipped), you must also have a program which opens .zip files) and register with the PrimeNet server, then you will be assigned numbers and you're set. What is a Mersenne Prime? Mersenne Primes are those primes who have the notation 2 p -1 where p is a prime number. Mersenne Primes are extremely rare, to date there is only 37 known Mersenne Primes, GIMPS has found the last three Mersenne Primes. List of all known Mersenne Primes! Milestones and Discoveries Thursday October 08, 1998 16:56:38 Joined GIMPS! Thursday October 15, 1998 20:01:14 Finished first factoring assignment. Wednesday October 28, 1998 17:16:00 -1 is divisble by 6939724926289389097 Eliminated 1 st exponent Saturday, November 28, 1998 10:27:15 Finshed first double-check assignment. -1 is composite.

44. List Of Mersenne Primes 1 st mersenne prime 2 2 1 Discovered Ancient times Dicoverer unknown Numberof digits 1 2 nd mersenne prime 2 3 -1 Discovered Ancient times Discoverer http://www.geocities.com/CapeCanaveral/Launchpad/4403/ListOfMP.html

List Of All Known Mersenne Primes st Mersenne Prime: 2 Discovered: Ancient times Dicoverer: unknown Number of digits: 1 nd Mersenne Prime: 2 Discovered: Ancient times Discoverer: unknown Number of digits: 1 rd Mersenne Prime: 2 Discovered: Ancient times Discoverer: unknown Number of digits: 2 th Mersenne Prime: 2 Discovered: Ancient times Discoverer: unknown Number of digits: 3 nd Mersenne Prime: 2 Discovered: 1456 Discoverer: anonymous Number of digits: 4 th Mersenne Prime: 2 Discovered: 1588 Discoverer: Cataldi Number of digits: 6 th Mersenne Prime: 2 Discovered: 1588 Discoverer: Cataldi Number of digits: 6 th Mersenne Prime: 2 Discovered: 1772 Discoverer: Euler Number of digits: 10 th Mersenne Prime: 2 Discovered: 1883 Discoverer: Pervushin Number of digits: 19 th Mersenne Prime: 2 Discovered: 1911 Discoverer: Powers Number of digits: 27 th Mersenne Prime: 2 Discovered: 1914 Discoverer: Powers Number of digits: 33 th Mersenne Prime: 2 Discovered: 1876 Discoverer: Lucas Number of digits: 39 th Mersenne Prime: 2 Discovered: 1952 Discoverer: Robinson Number of digits: 157 th Mersenne Prime: 2 Discovered: 1952 Discoverer: Robinson Number of digits: 183 th Mersenne Prime: 2 Discovered: 1952 Discoverer: Robinson Number of digits: 386 th Mersenne Prime: 2 Discovered: 1952 Discoverer: Robinson Number of digits: 664 th Mersenne Prime: 2 Discovered: 1952 Discoverer: Robinson Number of digits: 687 th Mersenne Prime: 2 Discovered: 1957 Discoverer: Riesel Number of digits: 969 th Mersenne Prime: 2 Discovered: 1961

45. 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.

46. Nuwen.net - Mersenne Primes Paper wrong (the ones that relate to current events), the Mersenne FAQ has changed locations,and I no longer believe in the existence of a hidden mersenne prime. http://nuwen.net/paper.shtml

nuwen.net - Mersenne Primes Paper All time would not suffice for the test De Novo: Links Culture Parrises Squares GeForce FX Reviews: Rating System Primary: bwtzip The Quotation Collection Downloads Anime/SF ... Deus Ex Diversions: Coloring Paper Airplane Origami Polyhedra Foundation Site Info: Archived News Personal Page Essays: Space Internet Programming C Intro ... Games Tech: C++ Computer Random Work PNG Random: Wallpaper Diet Book Reviews pngacc ... LASTLY About. really suggest that you go back to my secondary and primary sources; only cite things from my paper directly if you need to refer to my conjecture specifically.) The paper has been slightly altered from the version that was submitted to IB. I received an A for it in my IB Diploma. The paper itself, in zipped PDF format: mersenne.zip (266 KB) : Mersenne Primes: Development through History, Ongoing Work, and a New Conjecture http://nuwen.net/paper.shtml stl@nuwen.net Created October 1, 2000.

47. Mersenne The project is GIMPS, Great Internet mersenne prime Search. Thus thewhen a new mersenne prime is found, so is a new perfect number. http://www.fortunecity.com/meltingpot/manchaca/799/mersenne.html

web hosting domain names email addresses Mersenne Primes Mersenne primes deserve a special section on them, since they are the focus of a huge internet project that I am involved with. Remember that Mersenne primes are of the form: 2 n -1, where n is prime. The project is GIMPS , Great Internet Mersenne Prime Search. Here you can sign up for an exponent, n , to test. If your exponent creates a Mersenne prime, you will be famous, among the mathematicians and other prime number enthusiasts anyway. I am testing exponent 5,364,329. This exponent has a 1 in 43,969 chance of being a correct Mersenne exponent. I've got my fingers crossed. Laugh. But anyway, here is some information on Mersenne primes, beyond that which was in the Glossary. Early mathematicians thought that all numbers of the form 2 n -1 were prime, where n was prime. This is an easy mistake to understand when you consider that 2, 3, 5, 7 are, and 11 was basically beyond their calculating abilities until Hudalricus Regius showed that 2 -1=2047 wasn't in 1536 (23×89), By 1603 Pietro Cataldi had shown that 2 -1 and 2 -1 were both prime, but then incorrectly stated that 2

48. Frank's Great Internet Mersenne Prime Search Page mersenne prime Search Page de nic vu (www.nic.de.vu)P. http://gimps.de.vu/

Frank's Great Internet Mersenne Prime Search Page P Frank's Great Internet Mersenne Prime Search Page P

49. Mersenne Prime Definition Meaning Information Explanation mersenne prime definition, meaning and explanation and more about Mersenneprime. FreeDefinition - Online Glossary and Encyclopedia, mersenne prime. http://www.free-definition.com/Mersenne-prime.html

A B C D ... Contact Beta 0.71 powered by: akademie.de PHP PostgreSQL Google News about your search term 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 number s, 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

50. Mersenne Prime Search At TechDictionary.com mersenne prime Search. What is the Great Internet mersenne prime Search? Thoughouthistory, the largest known prime number has usually been a mersenne prime. http://www.techdictionary.com/resources/mersenne.html

Home Search Search Tips Domain List ... About/Site Map Mersenne Prime Search What is the Great Internet Mersenne Prime Search? You could discover one of the most coveted finds in all of Mathematics - a new Mersenne prime number. Join in on this fun, yet serious research project. All you need is a personal computer and a lot of luck. The Electronic Frontier Foundation is offering a $100,000 award to the first person to discover a ten million digit prime number! Later this year, we will make available free software where you can find such a prime number along with details on how the award money will be divided. The Great Internet Mersenne Prime Search (GIMPS) harnesses the power of thousands of small computers like yours to solve the seemingly intractable problem of finding HUGE prime numbers. Specifically, GIMPS looks for Mersenne Primes, expressed by the formula 2P-1. Over 8,000 people have contributed computer time to help discover world-record Mersenne primes. Thoughout history, the largest known prime number has usually been a Mersenne prime. Instructions: Step One: Download the free software You can join this search by downloading the free software provided. The search is coordinated by a central server, called

51. 39th Mersenne Prime Discovered 6, 2001 Michael Cameron, a 20 yearold volunteer in a worldwide research projectcalled the Great Internet mersenne prime Search (GIMPS), has discovered the http://alpha01.dm.unito.it/personalpages/cerruti/primi/primigrandi/39.html

Researchers Discover Largest Multi-Million-Digit Prime Using Entropia Distributed Computing Grid. -1 is now the Largest Known Prime. SAN DIEGO, California and ORLANDO, Florida, December 6, 2001 Michael Cameron, a 20 year-old volunteer in a worldwide research project called the Great Internet Mersenne Prime Search (GIMPS) , has discovered the largest known prime number using his PC and software by George Woltman and Entropia, Inc. as part of an international grid of more than 205,000 interconnected computers operated by the company. The new number, expressed in shorthand as 2 -1, contains 4,053,946 digits and was discovered November 14th. It belongs to a special class of rare prime numbers called Mersenne primes . The discovery marks only the 39th known Mersenne prime, named after Marin Mersenne , a 17th century French monk who studied the numbers. 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. Cameron used a 800 MHz AMD T-Bird PC running part-time for 45 days to prove the number prime. He said, "A friend informed me that if I was going to leave my computer on all the time I should make use of that wasted CPU time. I put GIMPS on my PC because it does not interfere with my work on the computer. Finding the new prime was a wonderful surprise!"

52. Mersenne Primtal Søgningen En koordineret søgning efter mersenne prime tal. Gratos software til rådighed. Listenover ofte stillede spørgsmål om mersenne prime programmet findes her. http://www.infohome.dk/mersenne/

i Danmark GIMPS GIMPS hjemmesider pÃ¥ 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?

53. LookSmart - Directory - Mersenne Prime Numbers mersenne prime Numbers Find different mathematical resources whichdiscuss this specific kind of prime number. Directory Listings http://search.looksmart.com/p/browse/us1/us317914/us328800/us1164188/us10022111/

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics Number Theory ... Prime Numbers Mersenne Prime Numbers - Find different mathematical resources which discuss this specific kind of prime number. Directory Listings About Internet PrimeNet Server Learn about and sign up to join this organization of mathematicians involved with the Great Internet Mersenne Prime Search. Mersenne and Fermat Primes Field Mathematician and author for this resource provides the main remarkable numbers of number theory. Check out various suggested resources. Mersenne Prime Digits and Names Mathematician and prime number expert offers decimal, English, and American expansions of known Mersenne primes. Includes recommended resources. Mersenne Primes: History, Theorems and Lists Contents include some historical notes, discussions about perfect numbers and different theorems, and a table of known Mersenne primes. Will Edgington's Mersenne Page Along with numerous recommended resources, the author offers factor data, newsletter archives, and proofs of theorems related to Mersenne primes. We're always looking for ways to improve your search experience.

54. Joe And The Great Internet Mersenne Prime Search (GIMPS) particular. George Woltman has organized the Great Internet MersennePrime Search, which I ve been a part of for several months. http://www.alumni.caltech.edu/~decker/prime.html

Searching for Big Prime Numbers I have always been a fan of large prime numbers, and Mersenne Primes in particular. George Woltman has organized the Great Internet Mersenne Prime Search , which I've been a part of for several months. He has over 17,000 people looking for the largest known prime numbers, using PCs. It's a great story, and a great use of those idle PC cycles. Since its inception, GIMPS has been responsible for finding the last three world-record prime numbers. Of course, I'm sure that the reason I've told you all this has nothing to do with my being one of the Top Producers, currently ranked just inside of the top hundred overall in terms of total contribution of compute cycles to Mersenne Prime finding ever. By the way, it only takes a few minutes to retrieve and install George's software on Windows, Linux, OS/2 or PowerMac systemsyou might want to give it a try and take a shot at entering the history books! For more information on Mersenne Primes and large primes, I'm pretty fond of the book The Little Book of Big Primes,

55. Mersenne Prime - InformationBlast mersenne prime Information Blast. mersenne prime. A mersenne primeis a prime number that is one less than a power of two. For example http://www.informationblast.com/Mersenne_prime.html

Mersenne prime 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; M n may be composite even though n is prime. For example, 2 Fast algorithms for finding Mersenne primes are available, and this is why the largest known prime numbers today are Mersenne primes.

56. Largest Known Mersenne Prime Largest known mersenne prime. mersenne primes are primes of the form . For tobe prime we must have that p is prime. is prime. It was discovered in 1997. http://db.uwaterloo.ca/~alopez-o/math-faq/node28.html

Next: Largest known prime Up: Prime Numbers Previous: Prime Numbers Largest known Mersenne prime Mersenne primes are primes of the form . For to be prime we must have that p is prime. is prime. It was discovered in 1997. Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

57. What Is The Current Status On Mersenne Primes? What is the current status on mersenne primes? The following mersenne primes areknown. The way to determine if is prime is to use the LucasLehmer test http://db.uwaterloo.ca/~alopez-o/math-faq/node35.html

Next: Formulae to compute prime Up: Prime Numbers Previous: List of record numbers What is the current status on Mersenne primes? The following Mersenne primes are known. The way to determine if is prime is to use the Lucas-Lehmer test: Lucas_Lehmer_Test(p): u := 4 for i from 3 to p do u := u^2-2 mod 2^p-1 od if u == then 2^p-1 is prime else 2^p-1 is composite fi All exponents less than 1,481,800 have now been tested at least once. References An introduction to the theory of numbers. G.H. Hardy, E.M. Wright. Fifth edition, 1979, Oxford. Alex Lopez-Ortiz Mon Feb 23 16:26:48 EST 1998

58. Mersenne Prime Numbers mersenne prime numbers are a special class of prime numbers that have the form,. A necessary condition for this number to be prime is that p is also prime. http://www2.potsdam.edu/millerrs/Mersenne.html

Roger's Homepage Team Stats Team Performnce Join Team ... Brian's Site Mersenne prime numbers are a special class of prime numbers that have the form, . A necessary condition for this number to be prime is that p is also prime. Out of all the tested exponents, only 39 Mersenne primes have been identified. It is an open question whether there is a finite or infinite number of primes of this form. GIMPS (the Great Internet Mersenne Prime Search) is a distributed computing project that is systematically testing possible candidates to find Mersenne Primes. Brian Jue , Assistant Professor of Mathematics at CSU Stanislaus, coordinates a team to participate in the search. Computers in the Math, Physics, and Chemistry Departments, some of the campus computer labs and many student computers have been recruited for the project. The program runs in the background at the lowest priority, so it doesn't interfere with any other tasks or degrade system performance. You can see how the team is doing by clicking on Team Stats . Click on Join Team to find out how you can contribute your spare computer cycles. For more information contact

59. Mersenne Primes And Fermat Primes A mersenne prime is a prime that is one less than a power of 2. Examples include3, 7, and 31. The exponent on a mersenne prime must also be prime. http://www.mathreference.com/num,mers.html

Numbers, Mersenne Primes and Fermat Primes Search Site map Contact us Join our mailing list ... Books Main Page Numbers Use the arrows at the bottom to step through Number Theory. Mersenne Primes and Fermat Primes A Mersenne prime is a prime that is one less than a power of 2. Examples include 3, 7, and 31. The exponent on a Mersenne prime must also be prime. To illustrate, consider 2 -1. Now 15 is not prime, infact it is 3×5, so replace 2 with 8, and write 8 -1. This is divisible by 8-1, just as x n -1 is divisible by x-1. If p is a Mersenne prime, say 2 k -1, then consider n = p×2 k-1 . Let's compute s (n). There is one instance of p, so the first component of s is 1+p. We know this better as 2 k . The second factor of n is 2, possibly raised to a high power. Hence the second component of s becomes 1+2+4+8+16+...+2 k-1 . This is equal to 2 k -1. We know this better as p. Therefore s (n) = 2 k ×p, which is twice n, hence n is a perfect number. Perfect numbers include 6, 28, and 496, corresponding to the first three Mersenne primes. conversely, suppose n is a perfect even number. Let n contain k-1 powers of 2. Thus

60. Mersenne Primes mersenne primes. The numbers M(q) = 2^q 1 (with q prime) are called Mersennenumbers. If M(q) = is prime then it is called a mersenne prime. http://pw1.netcom.com/~hjsmith/Perfect/Mersenne.html

Mersenne Primes N is an even perfect number if and only if N = 2^(q-1) * (2^q - 1) and 2^q - 1 is prime It should also be noted that for 2^q - 1 to be prime q must be prime. So when we search for even perfect numbers, we search on q equal to the primes. The numbers M(q) = 2^q - 1 (with q prime) are called Mersenne numbers. If M(q) = is prime then it is called a Mersenne prime. If a prime q makes a Mersenne number a Mersenne prime, then P(q) = 2^(q-1) * (2^q - 1) is a Perfect number. Here are the 39 known Mersenne primes, M(q), as of Nov 14, 2001: The way to determine if 2^q - 1 is prime, given that q is an odd prime, is to use the Lucas-Lehmer test: Lucas-Lehmer-Test(q): u := 4 for i := 3 to q do u := (u^2 - 2) mod (2^q - 1) enddo if u == then 2^q - 1 is prime else 2^q - 1 is composite endif EndTest Return to Perfect Numbers Return to Harry's Home Page This page accessed times since June 7, 1998.

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