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Topic: Mersenne prime

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Great Internet Mersenne Prime Search

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	Mersenne prime - Wikipedia, the free encyclopedia
		In mathematics, a Mersenne prime is a prime number that is one less than a prime 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.
		The best method presently known for testing the primality of Mersenne numbers is based on the computation of a recurring sequence, as developed originally by Lucas in 1878 and improved by Lehmer in the 1930s, now known as the Lucas-Lehmer test for Mersenne numbers.
	en.wikipedia.org /wiki/Mersenne_prime (868 words)

	Mersenne
		Mersenne, however, was devoted to study, which he loved, and, showing that he was ready for responsibilities of the world, had decided to further his education in Paris.
		Mersenne thought Galileo's assumption that a falling body passes through infinite degrees of speed was incompatible with a genuinely mechanistic explanation of acceleration.
		Mersenne was doubtful that the air pressure actually supported the mercury and on his return attempted to re-do the experiment but did not have the necessary equipment.
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Mersenne.html (2971 words)

	Mersenne prime
		Mersenne primes rank among the largest of all known primes because they have a particularly simple test for primality, called the Lucas-Lehmer test.
		They are named after Marin Mersenne who, in 1644, helped the search gain wide recognition by writing to many mathematicians of his conjecture about which small exponents yield primes.
		Around the time that Mersenne's conjecture was finally settled, in 1947, digital computers gave a new impetus to the hunt for Mersenne primes.
	www.daviddarling.info /encyclopedia/M/Mersenne_prime.html (313 words)

	Encyclopedia: Mersenne prime
		In mathematics, a prime number (or a prime) is a natural number greater than one whose only positive divisors are one and itself.
		In number theory, Lenstra, Pomerance, and Wagstaff have conjectured that not only are there an infinite number of Mersenne primes, meaning prime numbers of the form 2p − 1, but that the number of Mersenne primes with exponent p less than x is asymptotically approximated by, where γ is the Euler...
		Titanic prime is a term coined by Samuel Yates in the 1980s, denoting a prime number of more than 1000 decimal digits.
	www.nationmaster.com /encyclopedia/Mersenne-prime (3861 words)

	Will Edgington's Mersenne Page
		Prime exponent Mersenne numbers for which at least one LL test has been run and for which I have some factoring data but no factor are in DB.nf.
		The exponents of known Mersenne primes are in primeM.txt ; the complete factorizations known to me are in factoredM.txt (the largest prime factor is almost always implied, as some of them are _very_ large), and the roughly 6.7 MB lowM.txt contains the known information for all other Mersenne numbers with exponents less than 200,000.
		The status of Mersenne numbers with a Mersenne prime exponent (that is, M(M(p)) where M(p) = 2↑p - 1 is a Mersenne prime) is in MMPstats.txt.
	www.garlic.com /~wedgingt/mersenne.html (3423 words)

	Mersenne prime
		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.
		The best method presently known for testing the primality of Mersenne numbers is based on the computation of a recurring sequence, as developed originally by Lucas in 1878 and improved by Lehmer[?] in the 1930s.
	www.fastload.org /me/Mersenne_prime.html (429 words)

	Mersenne Prime Search
		The new prime was independently verified in 5 days by Tony Reix of Bull S.A. in Grenoble, France using 16 Itanium2 1.5 GHz CPUs of a Bull NovaScale 6160 HPC at Bull Grenoble Research Center, running the Glucas program by Guillermo Ballester Valor of Granada, Spain.
		The discovery is the ninth record prime for the GIMPS project.
		The first prime numbers are 2, 3, 5, 7, 11, etc. For example, the number 10 is not prime because it is divisible by 2 and 5.
	www.mersenne.org /prime.htm (1054 words)

	The Prime Glossary: Mersenne prime
		Mersenne Numbers are the easiest type of number to prove prime (because of the Lucas-Lehmer test), so are usually the largest primes on the list of largest known primes).
		Primes of this form were first studied by Euclid who explored their relationship with the even perfect numbers.
		Mersenne primes (sometimes just called Mersennes) are also generalized repunit primes and trivial circular primes (radix two).
	primes.utm.edu /glossary/page.php?sort=Mersennes (177 words)

	DCCentral [Great Internet Mersenne Prime Search] (Site not responding. Last check: 2007-11-07)
		Seven is a prime number; thus, three is a Mersenne prime.
		There have been only 38 Mersenne prime numbers found, and the GIMPS search is focusing on the large primes — numbers so huge that it could take your computer up to a year to crunch one exponent.
		The Mersenne prime search was formed in 1996, and —; ever since the project launched — a new world-record Mersenne prime has been discovered every year.
	library.thinkquest.org /C007645/english/2-mersenne-0.htm (510 words)

	Off the Kuff: New Mersenne prime found
		Mersenne primes are a special category, expressed as 2 to the "p" power minus 1, where "p" also is a prime number.
		This page has some good history about Mersenne primes as well as some of the math surrounding them, such as the proof that if (2^p)-1 is prime, then p must be prime.
		The discovery of a new Mersenne prime also means that we have discovered a new perfect number, too.
	www.offthekuff.com /mt/archives/002724.html (872 words)

	1918 News Service :: 42nd Mersenne Prime (Probably) Discovered
		If verified, this would be the 42nd known Mersenne prime, as well as the largest prime number known of any kind.
		Mersenne primes are intimately connected with so-called perfect numbers, which were extensively studied by the ancient Greeks, including by Euclid.
		The eight largest known Mersenne primes (including the latest candidate) have all been discovered by GIMPS, which is a distributed computing project being undertaken by an international collaboration of volunteers.
	news.1918.com /article.php?article_id=3161&type=comment (422 words)

	BBC News \| SCI/TECH \| Number takes prime position
		The prime number - a number that can only be divided by one and itself - was discovered by Michael Cameron, a 20-year-old Canadian participant in a mass computer project known as the Great Internet Mersenne Prime Search (Gimps).
		Mersenne primes are important for the theory of numbers and they may help in developing unbreakable codes and message encryptions.
		The study of Mersenne primes has been central to number theory since they were first discussed by Euclid in 350 BC.
	news.bbc.co.uk /1/hi/sci/tech/1693364.stm (802 words)

	Mersenne prime (Site not responding. Last check: 2007-11-07)
		Historically study of Mersenne primes was motivated by connection; in the 4th century BC Euclid demonstrated that if M is a prime then M(M+1)/2 is a perfect number.
		Fast algorithms for finding Mersenne primes are and this is why the largest known numbers today are Mersenne primes.
		The best method presently known for testing primality of Mersenne numbers is based on computation of a recurring sequence as developed by Lucas in 1878 and improved by Lehmer in the 1930s now known as the Lucas-Lehmer test.
	www.freeglossary.com /Mersenne_number (868 words)

	BBC NEWS \| Science/Nature \| Prime position for large number
		Primes are important to encryption and could lead to uncrackable codes.
		A prime is a number that can only be divided by one and itself.
		A Mersenne prime is a prime number of the form 2^P-1 (where the superscript "P" is the exponent, or number of times the original figure must be multiplied by itself).
	news.bbc.co.uk /1/hi/sci/tech/3256822.stm (617 words)

	Mersenne Primes: History, Theorems and Lists (Site not responding. Last check: 2007-11-07)
		It was obvious to Mersenne's peers that he could not have tested all of these numbers (in fact he admitted as much), but they could not test them either.
		The 25th and 26th Mersenne primes were found by high-school students Laura Nickel and Landon Curt Noll, who, though they had little understanding of the mathematics involved, used Lucas' simple test on the local university's mainframe (CSUH's CDC 174) to find the next two primes.
		Noll searched later, and though he never found another Mersenne prime, he is one of a team that holds the record for the largest non-Mersenne prime.
	www.utm.edu /research/primes/mersenne (1720 words)

	42nd Mersenne Prime Discovered
		Mersenne primes are most relevant only to number theorists.
		There may be smaller, as yet undiscovered Mersenne primes, and there certainly are larger Mersenne primes waiting to be discovered.
		Mersenne primes have been central to number theory since they were first discussed by Euclid in 350 BC.
	www.mersenne.org /25964951.htm (1196 words)

	Mersenne Prime Numbers (Site not responding. Last check: 2007-11-07)
		Mersenne prime numbers are numbers of the form
		The largest prime number known is a Mersenne prime number.
		Mersenne prime numbers have their own web site which is dedicated to a netwide search for Mersenne prime numbers and related tasks.
	www.math.utah.edu /~alfeld/math/mersenne.html (143 words)

	New Scientist Breaking News - 7-million digit prime number discovered
		Prime numbers are positive integers that can only be divided perfectly by themselves and one.
		It is the 41st Mersenne prime to have been found.
		A central server distributes different prime number candidates to each machine, which use spare processing power to test whether it is a genuine prime or not.
	www.newscientist.com /article.ns?id=dn5057 (421 words)

	The Speculist: Biggest Prime
		A key factor is that when such a prime is found, it's often not known whether there is a smaller Mersenne prime that just hasn't been discovered yet.
		What's key is that all prime exponents (a Mersenne prime is of the form 2^p -1 where p is prime) have been checked that are less than 10,412,700.
		It probably is a Mersenne prime that was found, simply because it's a known form, and there are some shortcut tests that can be used to verify it.
	www.speculist.com /archives/000468.html (463 words)

	Mersenne Prime Numbers (Site not responding. Last check: 2007-11-07)
		The concept of a Mersenne Prime is evolved from that of a perfect number.
		A Mersenne Prime is such a number Mp, where p is prime.
		A Mersenne Number is a number Mm which may or may not be prime.
	www.resort.com /~banshee/Info/mersenne.html (465 words)

	Ivars Peterson's MathTrek - Mersenne Megaprime
		The newly discovered number is the 38th known Mersenne prime, named for the French cleric and mathematician Marin Mersenne (1588-1648).
		However, because no one has yet checked all Mersenne numbers having smaller exponents, mathematicians can't be sure that no Mersenne primes lurk in the vast expanse between the record holder and the second-place Mersenne prime, which has an exponent of 3,021,377.
		Additional information about the Great Internet Mersenne Prime Search and the discovery of the 38th Mersenne prime is available at http://www.mersenne.org/prime.htm.
	www.maa.org /mathland/mathtrek_7_26_99.html (693 words)

	Biography of Marin Mersenne (Site not responding. Last check: 2007-11-07)
		Marin Mersenne is best known for his role as a sort of clearing house for correspondence between eminent philosophers and scientists, and for his work in number theory.
		The largest known prime is usually a mersenne prime.
		After the 23rd Mersenne prime was found at the University of Illinois, the mathematics department was so proud that they had their postage meter changed to stamp "2
	www.andrews.edu /~calkins/math/biograph/biomerse.htm (1044 words)

	Mersenne prime - a Whatis.com definition (Site not responding. Last check: 2007-11-07)
		A Mersenne (also spelled Marsenne) prime is a specific type of prime number.
		The first few known values of n that produce Mersenne primes are where n = 2, n = 3, n = 5, n = 7, n = 13, n = 17, n = 19, n = 31, n = 61, and n = 89.
		For this reason, Mersenne primes are of particular interest to developers of strong encryption methods.
	whatis.techtarget.com /definition/0,,sid9_gci788348,00.html (307 words)

	GIMPS MERSENNE PRIME WORLD RECORD LARGEST FOUND BY GORDON SPENCE
		Mersenne Prime at the time it was the world's largest known prime number.
		Stands for the Great Internet Mersenne Prime Search, and is a world wide project involving over 4500 participants (@ September 1998), coordinated by George Woltman who maintains the GIMPS site and Scott Kurowski who runs the Primenet Internet Server.
		For example, the number 10 is not prime because it is divisible by 2 and 5.
	www.rugeley.demon.co.uk /gimps/prime.htm (595 words)

	The Mersenne Prime Homepage
		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.
		George's goal is to test every Mersenne prime possibility up to 5,260,000 before the end of 1999.
	www.albanyconsort.com /mersenne (309 words)

	The Great Internet Mersenne Prime Search - The Perl Journal, Winter 1997
		Prime numbers are integers that can be evenly divided only by themselves and one.
		Since Mersenne was born, the highest known prime number since Mersenne was born has always been either a Mersenne prime or a factor of a Mersenne composite, except for a brief period in 1951.
		Currently 35 Mersenne numbers are known to be prime, and more are being tested even as you are reading these words.
	www.foo.be /docs/tpj/issues/vol2_4/tpj0204-0012.html (2036 words)

	Mersenne prime - InformationBlast
		More generally, Mersenne numbers (not necessarily primes, but candidates for primes) are numbers that are one less than an odd power of two; hence,
		As of May 2004, only 41 Mersenne primes were known; the largest known prime number (2
		It is not known whether any undiscovered Mersenne primes exist between M
	www.informationblast.com /Mersenne_prime.html (574 words)

	Word-of-the-Day: Mersenne prime
		The first few known values of n that produce Mersenne primes are n = 2, n = 3, n = 5, n = 7, n = 13, n = 17, n = 19, n = 31, n = 61, and n = 89.
		But the 'next' (unknown today, known tomorrow) prime is more difficult to find than the 'next' digit in the expansion of an irrational number.
		It takes the most powerful computer a long time to check a large number to determine if it is prime, and an even longer time to determine if it is a Mersenne prime.
	www.mail-archive.com /whatis@lists.techtarget.com/msg00176.html (463 words)

	Explananda: 41st Mersenne prime found?
		MathWorld is reporting that a computer participating in GIMPS, the Great Internet Mersenne Prime search, claims to have found the 41st Mersenne prime this morning.
		There's a $100,000 prize for the discovery of the first prime with 10 million digits, which GIMPS is likely to claim within a couple years.
		The discovery of the 41st Mersenne prime would also mean the discovery of the 41st perfect number.
	www.explananda.com /archives/000195.html (143 words)

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