41. Marin Mersenne - Wikipedia, The Free Encyclopedia Mersenne prime; Catalan–Mersenne number /Catalan's Mersenne conjecture; Equal temperament; Mersenne twister; Mersen; References ^ Murr, Sylvia, ed. (1997) (in French), Gassendi et l'Europe http://en.wikipedia.org/wiki/Mersenne

Marin Mersenne From Wikipedia, the free encyclopedia   (Redirected from Mersenne Jump to: navigation search For the primes named after Marin Mersenne, see Mersenne prime Marin Mersenne Born September 8, 1588 Oizé Maine Died Nationality French acoustics Marin Mersenne Marin Mersennus or le Père Mersenne (September 8, 1588 – September 1, 1648) was a French theologian philosopher mathematician and music theorist , often referred to as the "father of acoustics Bohn 1988 Contents Life Works Quaestiones celeberrimae in Genesim (1623) Other ... edit Life Marin Mersenne (pronounced Mehr-SENN) was born of peasant parents near Oizé Maine (present day Sarthe, France ). He was educated at Le Mans and at the Jesuit College of La Flèche . On July 17, 1611, he joined the Minim Friars , and, after studying theology and Hebrew in Paris received his full holy orders in 1613. Between 1614 and 1618, he taught theology and philosophy at Nevers , but he returned to Paris and settled at the convent of L'Annonciade in 1620. There, with other kindred spirits such as René Descartes Étienne Pascal Gilles de Roberval and Nicolas-Claude Fabri de Peiresc , he studied mathematics and music. He corresponded with

42. Mersenne Prime Digits Landon Curt Noll lists the decimal, English, and American expansions of all the known Mersenne primes. http://isthe.com/chongo/tech/math/prime/mersenne.html

43. Mersenne Prime Numbers The concept of a Mersenne Prime is evolved from that of a perfect number. A perfect number is an integer for which the sum of its divisors is twice the http://www.resort.com/~banshee/Info/mersenne.html

Mersenne Primes Marin Mersenne (1588-1648) was a Franciscan friar who lived most of his life in Parisian cloisters. He was the author of Cognitata Physico-Mathematica which stated without proof that M p is prime for p = 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, and 257 and for no other primes p for p < 257. It took over 300 years to totally settle this claim made by Mersenne. The final work done in 1947 showed that Mersenne made five errors in his work (namely that M is prime, M is composite, M is prime, M is prime, and M is composite). Besides his famous statement about primes of the form M p , Mersenne contributed to the development of number theory through his extensive correspondence with many mathematicians, including Fermat. Mersenne effectively served as a clearing house and a disseminator of new mathematical ideas in the 17th century. Kenneth Rosen, Elementary Number Theory; Addison Wesley The concept of a Mersenne Prime is evolved from that of a perfect number . A perfect number is an integer for which the sum of its divisors is twice the number. For example: (6) = 1 + 2 + 3 + 6 = 12 = 2*6 thus 6 is a perfect number.

44. DCCentral [Great Internet Mersenne Prime Search] Huge prime numbers are the bounty of the Great Internet Mersenne Prime Search. The search has been going on for four years now, and each year a recordbreaking prime is found http://library.thinkquest.org/C007645/english/2-mersenne-0.htm

45. SS > Factoids > Mersenne Prime 2 3 5 7 13 17 19 31 61 89 107 127 521 607 1279 2203 2281 3217 4253 4423 9689 9941 11 213 19 937 21 701 23 209 44 497 86 243 110 503 132 049 216 http://www-users.cs.york.ac.uk/~susan/cyc/m/mersenne.htm

@import url(../../stepney.css); home factoids Mersenne prime A prime number of the form where p is prime. The Mersenne number M p is prime for exponent p For all other prime exponents less than M p is composite, and for those less than 31,494,937 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, ...

46. Math Forum: Ask Dr. Math FAQ: Perfect Numbers Jump to What is a Mersenne Prime Number? A Mersenne Prime Number is a prime number that happens to also be a Mersenne Number. A Mersenne Prime Number http://mathforum.org/dr.math/faq/faq.perfect.html

Ask Dr. Math: FAQ P erfect N umbers Dr. Math FAQ Classic Problems Formulas Search Dr. Math ... Dr. Math Home What is a perfect number? How do you find them? How many are there? A contribution from John Knoderer, the MazeMan: What is a perfect number? How many perfect numbers are there? How many perfect numbers are known? Are there any odd perfect numbers? ... Your computer can join the search! What is a perfect number? A perfect number is a whole number, an integer greater than zero; and when you add up all of the factors less than that number, you get that number. Examples: The factors of 6 are 1, 2, 3 and 6. The factors of 28 are 1, 2, 4, 7, 14 and 28. The factors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496. The factors of 8128 are 1, 2, 4, 8, 16, 32, 64, 127, 254, 508, 1016, 2032, 4064 and 8128. I'll let you add them up. According to The Merriam-Webster Dictionary, the term was first used in the fourteenth century. The Grolier Multimedia Encyclopedia says that perfect numbers are "another example of Greek progress in number theory," and credits the Pythagoreans for coining the term "perfect." If you are interested in learning more about "perfect" numbers, you should also read up about "Mersenne" prime numbers because they are closely related. The first four perfect numbers were known over 2,000 years ago. Some ancient cultures gave mystic interpretations to numbers that they thought were magic.

47. MathWorld News: 44th Mersenne Prime Found Eric Weisstein's World of Mathematics Headline News MathWorld Headline News 44th Mersenne Prime Found By Eric W. Weisstein. September 11, 2006Less than a year after the 43rd Mersenne http://mathworld.wolfram.com/news/2006-09-11/mersenne-44/

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Headline News 44th Mersenne Prime Found By Eric W. Weisstein September 11, 2006Less than a year after the 43rd Mersenne prime was reported ( MathWorld headline news: December 25, 2005 ), the Great Internet Mersenne Prime Search (GIMPS) project has discovered the 44th known Mersenne prime. The candidate prime was flagged prime by Dr. Curtis Cooper and Dr. Steven Boone who, rather amazingly and against staggering odds, are also the discoverers of the 43rd known Mersenne prime, thus proving (in the words of the GIMPS website) that lightning can strike twice! Additional details can be found in the Mersenne.org press release Mersenne numbers are numbers of the form M n n - 1, giving the first few as 1, 3, 7, 15, 31, 63, 127, .... Interestingly, the definition of these numbers therefore means that the n th Mersenne number is simply a string of n 1s when represented in binary . For example, M is a Mersenne number. Mersenne primes are Mersenne numbers that are also prime , i.e., have no factors other than 1 and themselves. So, since the number 127 is prime and is a Mersenne number, it is a Mersenne prime.

48. Id:A000668 - OEIS Search Results It is easily proved that if n is a Mersenne prime then n+sigma(n)=sigma(sigma(n) ). Is it true that Mersenne primes are all the solutions of the equation http://www.research.att.com/njas/sequences/A000668

Greetings from The On-Line Encyclopedia of Integer Sequences Hints Search: id:A000668 Displaying 1-1 of 1 results found. page 1 short internal text references ... off Mersenne primes (of form 2^p - 1 where p is a prime). (Formerly M2696 N1080) list graph listen OFFSET COMMENT See for the values of p. Prime repunits in base 2. Define f(k) = 2k+1; begin with k = 2, a(n+1) = least prime of the form f(f(f(...(a(n)))). - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 26 2003 Mersenne primes other than the first are of form 6n+1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 27 2004 (a(n)) = and (a(n)+1) = 1. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 19 2004 Appears to give all n such that sigma(n+1)-sigma(n)=n - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 27 2002 If n is in the sequence then sigma(sigma(n))=2n+1. Is it true that this sequence gives all numbers n such that sigma(sigma(n))=2n+1? - Farideh Firoozbakht (mymontain(AT)yahoo.com), Aug 19 2005 Mersenne primes other than the first are of form 24n+7; see also

49. Mersenneforum.org A forum about prime numbers and computerized searches for more of them. Includes discussions of software and hardware issues encountered by searchers. http://www.mersenneforum.org/

mersenneforum.org User Name Remember Me? Password Register FAQ Calendar Search ... Mark Forums Read Welcome! If this is your first visit, be sure to check out the FAQ by clicking the link above. You may have to register before you can post: click the register link above to proceed. To start viewing messages, select the forum that you want to visit from the selection below. Forum Last Post Threads Posts New To GIMPS? Start Here! No registration required! (Posts are moderated.) Two worker threads, only one is saved by Unregistered 28 Oct 10 09:28 AM Homework Help No registration required! (Posts are moderated.) Odds that a Random Prime is a Number? by lorgix 13 Oct 10 10:31 AM Fun Stuff Lounge Sports Trivia by cheesehead 31 Oct 10 01:57 AM Puzzles 20 Questions - round 3 by lavalamp 31 Oct 10 02:55 AM Great Internet Mersenne Prime Search Software http://www.mersenne.org/freesoft.htm Prime95 version 25.11 by 29 Oct 10 04:16 PM Hardware Lucas–Lehmer on on ATI's GPUs (OpenCl or Stream) by fivemack 30 Oct 10 09:36 PM Math mersenne prime as a factor of another number by Damian 30 Oct 10 09:26 PM PrimeNet http://www.mersenne.org/primenet/

50. See The Largest Known Prime, All 13 Million Digits : NPR Apr 10, 2009 Currently, a Mersenne prime clocking in at nearly 13 million digits holds the So a team called the Great Internet Mersenne Prime Search, http://www.npr.org/templates/story/story.php?storyId=102871918

51. Rare Prime Number Found - Los Angeles Times Sep 27, 2008 The prize is being offered for finding the first Mersenne prime with more The new prime is the eighth Mersenne prime discovered at UCLA. http://articles.latimes.com/2008/sep/27/science/sci-prime27

52. Mersenne Prime | Facebook Welcome to the Facebook Community Page about Mersenne prime, a collection of shared knowledge concerning Mersenne prime. http://www.facebook.com/pages/Mersenne-prime/105942382769832

Mersenne prime 28 people like this. to connect with Wall Info Fan Photos Mersenne prime + Others Mersenne prime Just Others Mersenne prime joined Facebook. March 26 at 10:57pm See More Posts English (US) Español More… Download a Facebook bookmark for your phone. Login Facebook ©2010

53. Slashdot Science Story | 47th Mersenne Prime Confirmed radiot88 writes to let us know that he heard a confirmation of the discovery of the 47th known Mersenne Prime on NPR's Science Friday (audio here). The new prime, 2^42,643,801 1 http://science.slashdot.org/story/09/06/13/2218226/47th-Mersenne-Prime-Confirmed

54. Mersenne Primes - Phillips Exeter Academy Mathematics The 47th Mersenne prime M42643801 is a 12837064digit number. (6.12M) (out of order!) The 3rd Mersenne prime M5 = 31 is a 2-digit number. http://math.exeter.edu/rparris/mersenne.html

Mersenne Primes (30 June 09) To learn about Mersenne primes, visit GIMPS or MathWorld Wincalc will calculate and display these huge numbers. If you want to be able to see all the digits of a particularly large Mersenne prime, but do not want to tie up your computer for a couple of days, you can download self-extracting zip files: The 47th Mersenne prime is a 12837064-digit number. (6.12M) (out of order!) The 46th Mersenne prime is a 12978189-digit number. (6.19M) The 45rd Mersenne prime is a 11185272-digit number. (5.33M) The 44th Mersenne prime is a 9808358-digit number. (4.68M) The 43rd Mersenne prime is a 9152052-digit number. (4.36M) The 42nd Mersenne prime is a 7816230-digit number. (3.73M) The 41st Mersenne prime is a 7235733-digit number. (3.45M) The 40th Mersenne prime is a 6320430-digit number. (3.01M) The 39th Mersenne prime is a 4053946-digit number. (1.93M) The 38th Mersenne prime is a 2098960-digit number. (1.00M) The 37th Mersenne prime is a 909526-digit number. (444K) The 36th Mersenne prime is a 895932-digit number. (438K)

55. Mersenne Prime Search At TechDictionary.com ™ 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. http://www.techdictionary.com/resources/mersenne.html

Home Search Search Tips Domains ... Job Search NEW! Games HOT! Free Music+ COOL! Tech Stores NEW! Suggest A Term OS X Widget Trivia/Links Add To Your Site ... TakeYellow.com 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 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 Primenet . If you are worried about how this software might affect your computer, the University of Albany has written an excellent

56. MersennePrime It is necessary for n to be prime, but not every prime number n leads to a Mersenne prime 2n 1; for instance n=11 does not give a Mersenne prime. http://thesaurus.maths.org/dictionary/map/word/990

57. Number Gossip: List Of Properties This is not so, thus there is a separate entry for Mersenne prime numbers. Definition A Mersenne number which is also prime is called a Mersenne prime. http://www.numbergossip.com/list

Tanya Khovanova Number Gossip Properties abundant amicable apocalyptic power aspiring ... weird Abundant Definition: The number n is abundant if the sum of all its positive divisors except itself is more than n. They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers. First ten: There are 2487 abundant numbers below 10,000. Amicable Definition: The number n is amicable if it belongs to an amicable pair. Two numbers n and m are called an amicable pair if the sum of all positive divisors of n is equal to the sum of all positive divisors of m and both are equal to n + m. It all started with perfect numbers which are amicable with themselves. Those numbers adopted social virtues and qualities; for the parts of each of them have the power to generate the other. See also sociable numbers. First ten: There are 10 amicable numbers below 10,000. Apocalyptic power Definition: The number n is called an apocalyptic power if 2 n contains the consecutive digits 666 (in decimal). First ten: There are 6485 apocalyptic powers below 10,000.

58. The Mersenne Prime Homepage Mersenne Primes . Nayan Hajratwala, George Woltman, Scott Kurowski, et. al. found the largest Mersenne Prime ever! It is . It is believed to be the 38th Mersenne Prime. http://www.albanyconsort.com/mersenne/mersenne.html

Mersenne Primes Nayan Hajratwala, George Woltman , Scott Kurowski, et. al. found the largest Mersenne Prime ever! It is . It is believed to be the 38th Mersenne Prime. It was found by a program by the Great Internet Mersenne Prime Search My club, GIMPS , has the program, called Prime, or Prime 95, by George Woltman Visit the mailing list of Mersenne Primes . P. S. If you don't want a lot of e-mail DON'T click here. Yes. I'm a member of that, too. From one year to the next, the largest prime number is usually a Mersenne prime, because they are much easier to check. Mersenne primes, and Mersenne numbers in general, were discovered by the French monk Marin Mersenne, who is depicted in the picture above. There are two main ways to find these numbers: one is to use a supercomputer, such as a Cray T3E. The other way is get a lot of personal computers together. This is what George Woltman did. There are now over 6000 participants in George's Mersenne club. David Slowinsky might never find another Mersenne prime. George's club has found the last four: , and and has also completed various other search goals, such as proving that M32, 33, 34, and 35 are the numbers we originally expected that they were, by testing all the ones in between.

59. Mersenne Prime In mathematics, a Mersenne prime is a prime number that is one less than a prime power of two. For example, 31 (a prime number) = 32 − 1 = 25 − 1, and 5 also a prime number http://articles.gourt.com/en/Mersenne prime

Gourt Home Gourt Mersenne prime In mathematics , a Mersenne prime is a prime number that is one less than a prime 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 (most sources restrict the term Mersenne number to where n is prime as all Mersenne primes must be of this form as seen below) 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 exists (any that do have to belong to a significant number of special forms; see perfect number for more details). It is currently unknown whether there is an infinite number of Mersenne primes Searching for Mersenne primes The identity shows that M n can be prime only if n itself is prime, which simplifies the search for Mersenne primes considerably. The converse statement, namely that

60. Wolfram|Alpha For Educators What is Wolfram Alpha? Wolfram Alpha is a computational knowledge engine. It computes answers to specific questions on the fly using its builtin algorithms http://www.wolframalpha.com/educators/

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