1. Mersenne Prime - Wikipedia, The Free Encyclopedia A Mersenne prime is a Mersenne number that is prime. It is known that if 2p 1 is prime then p is prime, so it makes no difference which Mersenne number http://en.wikipedia.org/wiki/Mersenne_prime

Mersenne prime From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , a Mersenne number , named after Marin Mersenne , is a positive integer that is one less than a power of two Some definitions of Mersenne numbers require that the exponent p be prime. A Mersenne prime is a Mersenne number that is prime . It is known that if 2 p p is prime, so it makes no difference which Mersenne number definition is used. As of October 2009 [ref] , only 47 Mersenne primes are known. The largest known prime number − 1) is a Mersenne prime. Since 1997, all newly-found Mersenne primes have been discovered by the " Great Internet Mersenne Prime Search " (GIMPS), a distributed computing project on the Internet. Contents About Mersenne primes Searching for Mersenne primes Theorems about Mersenne numbers History ... edit About Mersenne primes Unsolved problems in mathematics Are there infinitely many Mersenne primes? Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether the set of Mersenne primes is finite. The Lenstra–Pomerance–Wagstaff conjecture asserts that, on the contrary, there are infinitely many Mersenne primes and predicts their

2. Mersenne Primes - Wikiversity 109 649037107316853453566312041152511 113 10384593717069655257060992658440191 127 170141183460469231731687303715884105727 Eleventh Mersenne prime http://en.wikiversity.org/wiki/Mersenne_primes

Mersenne primes From Wikiversity Jump to: navigation search Welcome to the Wikiversity Mersenne Primes Learning Project Marin Mersenne's name is widely known because of his interest in prime numbers that are one less than a power of two. Mersenne also did research in the area of the theory of music and musical instruments (see Wikipedia ). Participants in this learning project are encouraged to join the distributed computing project that allows the computing power of personal computers to help search for Mersenne prime numbers (see Research Project , below). Contents Mersenne prime numbers To find Mersenne primes Research Project See also ... edit Mersenne prime numbers In Mathematics , Mersenne prime numbers are those prime numbers which are one less than a power of two. if is not a prime number, then can be written as, This implies, the Mersenne number is not a prime number if n is not prime. edit To find Mersenne primes Prime factors First Mersenne prime Second Mersenne prime Third Mersenne prime Fourth Mersenne prime Fifth Mersenne prime Sixth Mersenne prime Seventh Mersenne prime Eighth Mersenne prime Ninth Mersenne prime Tenth Mersenne prime Eleventh Mersenne prime edit Research Project Join the Great Internet Mersenne Prime Search . Describe your experience below. edit See also Mersenne wiki Retrieved from " http://en.wikiversity.org/wiki/Mersenne_primes

3. Mersenne Prime - Definition In mathematics, a Mersenne prime is a prime number that is one less than a power of two. For example, 3 = 4 1 = 2 2 1 is a Mersenne prime; http://www.wordiq.com/definition/Mersenne_prime

Mersenne prime - Definition 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 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.

4. Mersenne Prime - Simple English Wikipedia, The Free Encyclopedia A Mersenne prime is a Mersenne number that is a prime number. ,The exponent http://ja.wikipedia.org/wiki/simple:Mersenne_prime

Mersenne prime From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , a Mersenne number is a number that is one less than a power of two M n n A Mersenne prime is a Mersenne number that is a prime number . ,The exponent n must be prime too. This however, is not sufficient. Many mathematicians prefer the definition of a Mersenne number where n has to be a prime number. For example, , and 5 is a prime number, so 31 is a Mersenne number; and 31 is also a Mersenne prime because it is a prime number. But the Mersenne number is not a prime because it is divisible by 89 and 23. And can be shown to be composite because 4 is not prime. Throughout modern times, the largest known prime number has very often been a Mersenne prime. 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 numbers , which are numbers 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. In the 18th century

5. Answers.com - What Is A Mersenne Prime A Mersenne Prime is when 2^n1 is prime. Some examples of a Mersenne Prime are n=2,3,5,7,13,17,19,31,61,89,107, and 127 http://wiki.answers.com/Q/What_is_a_Mersenne_prime

6. Mersenne Prime: Facts, Discussion Forum, And Encyclopedia Article Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from http://www.absoluteastronomy.com/topics/Mersenne_prime

Home Discussion Topics Dictionary ... Login Mersenne prime Mersenne prime Topic Home Discussion Discussion Ask a question about ' Mersenne prime Start a new discussion about ' Mersenne prime Answer questions from other users Full Discussion Forum Encyclopedia In mathematics Mathematics Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions.... , a Mersenne number , named after Marin Mersenne Marin Mersenne Marin Mersenne, Marin Mersennus or le Père Mersenne was a French theologian, philosopher, mathematician and music theorist, often referred to as the "father of acoustics" .-Life:... , is a positive integer that is one less than a power of two Power of two In mathematics, a power of two is any of the integer powers of the number two; in other words, two multiplied by itself a certain number of times. By definition, the number one is a power of two.... Some definitions of Mersenne numbers require that the exponent p be prime.

7. Mersenne Prime - Simple English Wikipedia, The Free Encyclopedia In mathematics, a Mersenne number is a number that is one less than a power of two. A Mersenne prime is a Mersenne number that is a prime number. ,The exponent n must be prime too. http://simple.wikipedia.org/wiki/Mersenne_prime

Mersenne prime From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics , a Mersenne number is a number that is one less than a power of two M n n A Mersenne prime is a Mersenne number that is a prime number . ,The exponent n must be prime too. This however, is not sufficient. Many mathematicians prefer the definition of a Mersenne number where n has to be a prime number. For example, , and 5 is a prime number, so 31 is a Mersenne number; and 31 is also a Mersenne prime because it is a prime number. But the Mersenne number is not a prime because it is divisible by 89 and 23. And can be shown to be composite because 4 is not prime. Throughout modern times, the largest known prime number has very often been a Mersenne prime. 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 numbers , which are numbers 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. In the 18th century

8. 45th Mersenne Prime Revealed • The Register Numberporn lovers rejoice! The most ridiculously long prime number ever discovered has been verified and revealed in all its 12-million-digit glory. http://www.theregister.co.uk/2009/10/14/45th_mersenne_prime_verified_revealed/

9. Wapedia - Wiki: Mersenne Prime Apr 12, 2009 A Mersenne prime is a Mersenne number that is prime. It is known that if 2p 1 is prime then p is prime so it makes no difference which http://wapedia.mobi/en/Mersenne_prime

Wiki: Mersenne prime In mathematics , a Mersenne number , named after Marin Mersenne , is a positive integer that is one less than a power of two Some definitions of Mersenne numbers require that the exponent p be prime. A Mersenne prime is a Mersenne number that is prime . It is known that if 2 p − 1 is prime then p is prime, so it makes no difference which Mersenne number definition is used. As of October 2009 [ref] , only 47 Mersenne primes are known. The largest known prime number − 1) is a Mersenne prime. Since 1997, all newly-found Mersenne primes have been discovered by the " Great Internet Mersenne Prime Search " (GIMPS), a distributed computing project on the Internet. Contents: 1. About Mersenne primes 2. Searching for Mersenne primes 3. Theorems about Mersenne numbers 4. History ... 12. External links 1. About Mersenne primes Unsolved problems in mathematics Are there infinitely many Mersenne primes? Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether the set of Mersenne primes is finite. The Lenstra-Pomerance-Wagstaff conjecture asserts that, on the contrary, there are infinitely many Mersenne primes and predicts their

10. Mersenne Prime On GetGlue In mathematics, a Mersenne number is a positive integer that is one less than a power of two Some definitions of Mersenne numbers require that the exponent n be prime. A http://getglue.com/topics/p/mersenne_prime

GetGlue Login Hi! This is a topic page on Glue! Glue is a free service connecting your friends and fans around entertainment you love. Check-in and rate things to discover new favorites, get stickers and win free stuff. Join now! takes 30 seconds Visits Likes Check-ins Just Checked-in You are thinking about this Just Now Obsessed? Feature this on your profile Apps Check-in to your entertainment on iPhone, iPad, Android and more with GetGlue Apps Get the Latest News Blog Twitter Tooltip I like it More Mersenne prime Mersenne prime In mathematics, a Mersenne number is a positive integer that is one less than a power of two: Some definitions of Mersenne numbers require that the exponent n be prime. A Mersenne prime is a Mersenne number that is prime. As of June 2009[ref], only 47 Mersenne primes are known; the largest known prime number (243,112,609 − 1) is a Mersenne... more In mathematics, a Mersenne number is a positive integer that is one less than a power of two: Some definitions of Mersenne numbers require that the exponent n be prime. A Mersenne prime is a Mersenne number that is prime. As of June 2009[ref], only 47 Mersenne primes are known; the largest known prime number (243,112,609 − 1) is a Mersenne prime, and in modern times, the largest known prime has almost always been a Mersenne prime. Similar to things you like: Share Facebook Twitter Tell Friends Recent ... Top Rated People Who Liked This Reeya Kataria Alek Stoll Richard Kunkel eugene ... John E.L. Tenney

11. Mersenne Prime A prime number of the form 2 p 1, where p is prime. A prime exponent is necessary for a Mersenne number to be prime but is not sufficient; for example, 2 11-1 = 2,047 = 23 89 http://www.daviddarling.info/encyclopedia/M/Mersenne_prime.html

TYPES OF NUMBER PRIME NUMBERS A B ... CONTACT entire Web this site Mersenne prime A prime number of the form 2 p - 1, where p is prime. A prime exponent is necessary for a Mersenne number to be prime but is not sufficient; for example, 2 p , further occurrences become increasingly rare. At the time of writing there are 40 known Mersenne primes, corresponding to values for p of 2; 3; 5; 7; 13; 17; 19; 31; 61; 89; 107; 127; 521; 607; 1,279; 2,203; 2,281; 3,217; 4,253; 4,423; 9,689; 9,941; 11,213; 19,937; 21,701; 23,209; 44,497; 86,243; 110,503; 132,049; 216,091; 756,839; 859,433; 1,257,787; 1,398,269; 2,976,221; 3,021,377; 6,972,593; 13,466,917; and 20,996,011; however, it isn't known if the current largest Mersenne prime is the fortieth in order of size because not all lower exponents have been checked. Mersenne primes rank among the largest of all known primes because they have a particularly simple test for primality, called the Lucas-Lehmer test The search for Mersenne primes has been going on for centuries. They are named after Marin

12. Mersenne Prime Mersenne prime. A Mersenne prime is a prime number that is one less than a power of two. For example, 3 = 4 − 1 = 2 2 − 1 is a Mersenne prime; so is 7 = 8 − 1 = 2 3 − 1. 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

13. Mersenne Prime - Exampleproblems In mathematics, a Mersenne prime is a prime number that is one less than a power of two. For example, 3 = 4 − 1 = 2 2 − 1 is a Mersenne prime; so is 7 = 8 − 1 = 2 3 − 1. http://www.exampleproblems.com/wiki/index.php/Mersenne_prime

Mersenne prime From Exampleproblems Jump to: navigation search 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 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 exists. It is currently unknown whether there is an infinite number of Mersenne primes Contents Properties of Mersenne numbers Searching for Mersenne primes List of Mersenne primes See also ... External links Properties of Mersenne numbers Mersenne numbers share several properties: M n is a sum of binomial coefficients If a is a divisor of M q (q prime) then a has the following properties: : and: A theorem from Euler about numbers of the form shows that M q (q prime) is a prime if and only if there exists only one pair x y such that: M q x y with . More recently, Bas Jansen has studied

14. Talk:Mersenne Prime - Definition It is easy to see that 2 p1 is prime iff p is prime I'm not sure its really easy at all maybe I'll wait for the proof to come up on the Prime numberss page; but in the http://www.wordiq.com/definition/Talk:Mersenne_prime

Talk:Mersenne prime - Definition It is easy to see that 2 p -1 is prime iff p is prime... I'm not sure its really easy at all... maybe I'll wait for the proof to come up on the Prime numberss page; but in the mean time, the sentence should be reworded for a regular guy (like me) to know whats going on. cM It is not hard. If p is not prime, then you can write p as qr. It is easy to see that 2^q-1 and 2^r-1 are then divisors of 2^p-1 and therefore 2^p-1 is not prime either. The reason is obvious if you write 2^p-1 in the binary form. It looks like the digit "1" repeated p times (1111...). Similarly, 2^q-1 is the number 1 repeated q times. For example, 2^15-1 is 111111111111111, and 2^3-1 is 111, and the latter is obviously a divisor of the former because the ratio is 1001001001001. See also my text at the bottom. Lumidek 14:04, 6 Jun 2004 (UTC) Ok, I'll reword it. In fact, "iff" is wrong. If p -1 is prime, then p must itself be prime. Axel "Iff" being the abbreviation used in logic for "if and only if"? Yes.

15. GIMPS Home Online search for Mersenne prime numbers, found largest several primes. http://www.mersenne.org/

16. Mersenne Primes: History, Theorems And Lists Definition When 2 n1 is prime it is said to be a Mersenne prime. It was obvious to Mersenne's peers that he could not have tested all of these numbers (in fact he admitted as http://primes.utm.edu/mersenne/

Mersenne Primes: History, Theorems and Lists Our book " Prime Curios! The Dictionary of Prime Number Trivia " is now available on CreateSpace Amazon Contents: Early History Perfect Numbers and a Few Theorems Table of Known Mersenne Primes The Lucas-Lehmer Test and Recent History ... Conjectures and Unsolved Problems See also Where is the next larger Mersenne prime? and Mersenne heuristics For remote pages on Mersennes see the Prime Links' Mersenne directory Primes: Home Largest Proving How Many? ... Mailing List 1. Early History Many early writers felt that the numbers of the form 2 n -1 were prime for all primes n , but in 1536 Hudalricus Regius showed that 2 -1 = 2047 was not prime (it is 23 89). By 1603 Pietro Cataldi had correctly verified that 2 -1 and 2 -1 were both prime, but then incorrectly stated 2 n -1 was also prime for 23, 29, 31 and 37. In 1640 Fermat showed Cataldi was wrong about 23 and 37; then Euler in 1738 showed Cataldi was also wrong about 29. Sometime later Euler showed Cataldi's assertion about 31 was correct. Enter French monk Marin Mersenne (1588-1648). Mersenne stated in the preface to his

17. Mersenne Prime -- From Wolfram MathWorld A Mersenne prime is a Mersenne number, i.e., a number of the form M_n=2^n1, that is prime. In order for M_n to be prime, n must itself be prime. This is true since http://mathworld.wolfram.com/MersennePrime.html

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

19. Why 2 To The Power Of 43,112,609 - 1 = $100,000 For Prime Number Hunters | Scien Sep 29, 2008 Computer scientists utilise downtime on volunteers' PCs to search for Mersenne prime in bid to win prize http://www.guardian.co.uk/science/2008/sep/29/maths

document.domain = "guardian.co.uk"; Turn autoplay off Turn autoplay on Please activate cookies in order to turn autoplay off Jump to content [s] Jump to site navigation [0] Jump to search [4] Terms and conditions [8] ... Register Text larger smaller About us About us Contact us Press office Guardian Print Centre ... Subscribe Today's paper The Observer Comment Sport New Review ... Observer Food Monthly Zeitgeist Today's hot topics guardian.co.uk Science Web News Sport Comment Culture ... Science Why 2 to the power of 43,112,609 - 1 = $100,000 for prime number hunters Tweet this James Randerson , science correspondent The Guardian Monday 29 September 2008 Computer scientists are hoping to claim a $100,000 prize after discovering the largest known prime number. At 12,978,189 digits long, it would take the best part of two and a half months to write out by hand. Prime numbers, which can only be divided by one and themselves, have long fascinated mathematicians as the building blocks of other numbers. They are now central to techniques used to encrypt data such as credit card details as they are sent around the internet. The new prime was discovered by Edson Smith of the University of California Los Angeles mathematics department. He installed software on to the department's computers from the Great Internet Mersenne Prime Search (Gimps), which uses downtime on volunteers' PCs to hunt for ever larger prime numbers. Around 100,000 computers add up to what has been called a "grassroots supercomputer" that performs 29 trillion calculations a second.

20. Will Edgington's Mersenne Page Files with Mersenne factors. Includes proofs of theorems related to the search for Mersenne primes and factors. http://www.garlic.com/~wedgingt/mersenne.html

Quick links to other Mersenne related files on my site update.txt : Date of last update of the data files. M3status.txt : Data about factorization of M(p) - 2 for prime M(p). Mersenneplustwo : Other web site with data about factors of M(p) + 2. MMPstats.txt : Data about factorization of M(M(p)) for prime M(p). facntD.txt : Factor counts for completely factored M(n) for all n > 1. facntHU.txt : Factor counts for incompletely factored M(n), n > 1. facpriks.txt : List of files with all known factors for M(p) for primes p, M(p) not factored. results.pfk.split.aa.bz2 : First file listed in facpriks.txt. Links to rest of the pieces. factoredM.txt : All known factors for M(n) for all M(n) completely factored. mersdata.zip : lowM.txt, DATABASE, DB.nf, primeM.txt, factoredM.txt, etc., zipped mersfmt.txt : Description of data format used in lowM.txt, factoredM.txt, etc. newsletters.html : All of George Woltman's GIMPS newsletters. primeM.txt : List of primes p for which M(p) is known to be prime. querylang.txt : Old draft of Mersenne data query language. Quick links to other Mersenne and Prime number related sites Mersenne Prime Project (GIMPS: George Woltman) Chris Caldwell's Prime numbers pages Chris Caldwell's Mersenne pages Ernst Mayer's programs ... ECPP and other info (Francois Morain) in French and in English Cunningham Project (Paul Leyland) and a mirror Machine-readable Cunningham Tables by Jeroen Demeyer.

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