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Topic: Mersenne

	Mersenne biography
		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/Biographies/Mersenne.html (2965 words)

	PlanetMath: Mersenne numbers
		Mersenne primes have a strong connection with perfect numbers.
		It is conjectured that the density of Mersenne primes with exponent
		This is version 13 of Mersenne numbers, born on 2001-10-18, modified 2006-09-11.
	planetmath.org /encyclopedia/MersenneNumbers.html (163 words)

	Marin Mersenne Biography \| World of Mathematics
		Mersenne was born on September 8, 1588, near Oize, Sarthe, France, and later entered into service for the Roman Catholic Church as a devoted teacher in 1611.
		Even though Mersenne was not successful in his attempt to create an ironclad formula, his conjectures were the stimulus and basis for later research into the theory of numbers and the search for large prime numbers (called Mersenne primes).
		Mersenne spent his life as a staunch supporter of experimentation and was indirectly responsible for the invention of the pendulum clock.
	www.bookrags.com /biography/marin-mersenne-wom (862 words)

	CATHOLIC ENCYCLOPEDIA: Marin Mersenne
		Mersenne entered the novitiate of the Minims at Nigeon near Paris (1611), was sent to Nevers as professor of philosophy (1614-1620), and returned to Paris.
		Mersenne's suspicions; but Descartes's answers to his critics gave him full satisfaction as to his friend's orthodoxy and sincere Christian spirit.
		Mersenne asked that, after his death, an autopsy be made on his body, so as to serve to the last the interests of science.
	www.newadvent.org /cathen/10209b.htm (293 words)

	Mersenne prime - Mersennewiki (Site not responding. Last check: 2007-10-22)
		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.
		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.
	mersennewiki.org /index.php/Mersenne_prime (587 words)

	Mersenne prime - 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 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 (874 words)

	The Bassoons in Marin Mersenne's Harmonie universelle (1636)
		As a result, Mersenne traditionally has been considered one of the final exponents of the older instruments, and his descriptions of woodwinds have served as a point of departure, a source to which discussions of remodelled instruments may be compared.
		However, Mersenne must be referring to the natural range of the bassoon; as with other free-blown double reeds of the time, increasing the breath and adjusting the embouchure increased the range by at least an octave.
		The final innovation on Mersenne's fagot is the third key, which we have suggested controlled the note C. The three- keyed bassoon became the standard variety of the late seventeenth and early eighteenth centuries.
	www.idrs.org /Publications/DR/DR10.2/DR10.2.Semm.html (2878 words)

	The Galileo Project
		Mersenne is most well-known for his network of correspondents.
		From 1623 Mersenne began to make the careful selection of savants who met at his convent in Paris or corresponded with him from all over Europe and as far afield as Tunisia, Syria, and Constantinople.
		It was in Mersenne's quarters that in 1647 the young Blaise Pascal met Descartes.
	galileo.rice.edu /Catalog/NewFiles/mersenne.html (891 words)

	Mersenne Primes: History, Theorems and Lists (Site not responding. Last check: 2007-10-22)
		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.
		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 "2^11213-1 is prime" on each envelope.
		The 25th and 26th Mersenne primes were found by high-school students Laura Nickel and Curt Noll, who, though they had no understanding of the mathematics involved, used Lucas' simple test on the local university's mainframe (CSUH's CDC 720) to find the next two primes.
	cage.rug.ac.be /~hvernaev/mersenne.shtml (1397 words)

	Marin Mersenne - Wikipedia, the free encyclopedia
		Marin Mersenne, Marin Mersennus or le Père Mersenne (September 8, 1588 – September 1, 1648) was a French theologian, philosopher, mathematician and music theorist.
		Marin Mersenne (pronounced Mayr-senn) was born of peasant parents near Oizé, Maine (present day Sarthe).
		Mersenne is remembered today thanks to his association with the Mersenne primes.
	en.wikipedia.org /wiki/Marin_Mersenne (663 words)

	Mersenne Primes (Site not responding. Last check: 2007-10-22)
		A Mersenne prime is a Mersenne number which is also a prime number.
		Mersenne numbers are named after French monk Father Marin Mersenne, who proposed an assertion about the primality of a certain class of numbers.
		Mersenne prime numbers have been the largest prime numbers found to date over the past few years.
	www.contrib.andrew.cmu.edu /~svun/math/primes.htm (1308 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.
		Mersenne (pronounced mehr-SANE, named for a 17th century French monk/amateur mathematician Marin Mersenne, who was also a regular correspondent of Pierre Fermat) primes are cool, if you're into numbers.
		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.
	www.offthekuff.com /mt/archives/002724.html (872 words)

	The Mersenne Twister
		The invention of the Mersenne Twister was preceded by the development, by the same inventors, of a related algorithm with an array of 25 rather than 624 elements, called TT800.
		Many Mersenne primes are known; a list of them is available at this site, and it may also be noted that there is a relationship between the Mersenne primes and the perfect numbers.
		The first of the Mersenne primes to be discovered by computer were 2^521-1, 2^607-1, 2^1279-1, 2^2203-1, and 2^2281-1, all discovered by Raphael M. Robinson on the Standards Western Automatic Computer (SWAC) a computer with a small Williams Tube random-access memory and a larger auxilliary memory on a magnetic drum.
	www.quadibloc.com /crypto/co4814.htm (3755 words)

	BBC News \| SCI/TECH \| Number takes prime position
		Mersenne primes are important for the theory of numbers and they may help in developing unbreakable codes and message encryptions.
		A Mersenne prime is a prime of the form 2
		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
		Mersenne primes deserve a special section on them, since they are the focus of a huge internet project that I am involved with.
		If your exponent creates a Mersenne prime, you will be famous, among the mathematicians and other prime number enthusiasts anyway.
		Thus the when a new Mersenne prime is found, so is a new perfect number.
	www.fortunecity.com /meltingpot/manchaca/799/mersenne.html (624 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 8 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 (3485 words)

	43rd Mersenne Prime Discovered
		The new prime is the 43rd discovery in a special class of rare prime numbers known as Mersenne primes, named for French monk Marin Mersenne, who studied these numbers more than 350 years ago.
		The first Mersenne primes are 3, 7, 31, and 127 corresponding to P = 2, 3, 5, and 7 respectively.
		Mersenne primes have been central to number theory since they were first discussed by Euclid in 350 BC.
	www.mersenne.org /30402457.htm (1323 words)

	Mersenne primes (Site not responding. Last check: 2007-10-22)
		Mersenne numbers are named for the French mathematician Marin Mersenne (1588-1648), who studied them.
		Mersenne showed that if (2^p) - 1 is prime, then p must be prime (the converse is not true, e.g.
		Nowadays, most of the interest in Mersenne numbers is connected with the search for larger and larger prime numbers.
	www.newton.dep.anl.gov /newton/askasci/1995/math/MATH037.HTM (373 words)

	BBC - h2g2 - Mersenne Numbers
		Marin Mersenne (1588 - 1648) was a French monk, philosopher and mathematician of the 17th Century.
		Mersenne himself made many discoveries, including the use of a pendulum as a regulator in clocks.
		A Mersenne number that is prime is known as a Mersenne prime.
	www.bbc.co.uk /dna/h2g2/A670051 (2017 words)

	MathWorld News: 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.
	www.lehigh.edu /~bad0/bdNews42ndMers3.html (433 words)

	40th Mersenne Prime Is Discovered
		The discovery is not only the largest Mersenne prime but also the largest known prime number to date.
		This is the third Mersenne found in 1 ¼ years (as announced in earlier issues of REC), so others and I are not giving it as much play as in the past.
		Mersenne primes are an especially rare type of prime, namely a prime number of the form 2
	members.aol.com /DrMWEcker/Mersenne.htm (1683 words)

	Mersenne Prime Numbers (Site not responding. Last check: 2007-10-22)
		Marin Mersenne (1588-1648) was a Franciscan friar who lived most of his life in Parisian cloisters.
		The concept of a Mersenne Prime is evolved from that of a perfect number.
		A Mersenne Number is a number Mm which may or may not be prime.
	www.resort.com /~banshee/Info/mersenne.html (465 words)

	Mersenne Primes: History, Theorems and Lists
		We put question marks instead of a number for the the last of the Mersenne primes because it will not be known if there are other Mersenne's in between these until a check and double check has been completed by GIMPS.
		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.
		Slowinski, who works for Cray computers, has written a version of the Lucas test that he has convinced many Cray labs around the world to run in their spare time (time that would be lost otherwise).
	primes.utm.edu /mersenne (1727 words)

	Mersenne Twister Random Number Generator (Site not responding. Last check: 2007-10-22)
		The Mersenne Twister is an algorithm for generating random numbers.
		I have implemented the Mersenne Twister in a C++ class that is fast, convenient, portable, and free.
		The seeding algorithm was revised to correct a minor problem in which the highest bit of the seed was not well represented in the generator state.
	www-personal.engin.umich.edu /~wagnerr/MersenneTwister.html (264 words)

	Biography of Marin Mersenne
		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.
		Mersenne had many meetings in his home with Fermat, Pascal, Gassendi, Roberval, Beaugrand, and others who became prominent mathematicians such as Mersenne.
		In 1633, Mersenne published Traite de mouvments, and in 1634 he published Les Mechanique de Galile, which was a version of Galileo's lectures on mechanics.
	www.andrews.edu /~calkins/math/biograph/biomerse.htm (1044 words)

	Mersenne Priemgetal - Mersenne Pirme
		Mersenne primes were first studied because of the remarkable properties that every Mersenne prime corresponds to exactly one
		Almost exactly six months later, discovery of the 41st known Mersenne prime by a GIMPS volunteer was announced.
		Discovery of the 42nd known Mersenne prime was announced by Woltman on Feb. 18, 2005, but has yet to be confirmed.
	users.skynet.be /fa956617/math/topics/MersennePrime.html (770 words)

	Mathematica and Mersenne Primes
		Mersenne primes have long played an important role in number theory--for example, in the theory of so-called perfect numbers and in cryptography, where certain algebraic fields enjoy efficient, Mersenne-based arithmetic.
		Though Mersenne primes have been studied for centuries, many fundamental questions remain, including whether an infinite number of them exist.
		The only way to determine whether a very large number is really prime is to run a so-called primality test, which in the case of Mersenne primes can be an efficient manifestation called the Lucas-Lehmer test.
	www.wolfram.com /news/mersenne.html (406 words)

	The Mersenne Prime Homepage
		It is believed to be the 38th Mersenne Prime.
		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.
	www.albanyconsort.com /mersenne/mersenne.html (269 words)

	SS > factoids > Mersenne prime
		Mersenne numbers have a particulary simple test for primality, the Lucas-Lehmer test.
		Each Mersenne prime corresponds to an even perfect number.
		Not all the non-prime Mersennes have been completely factored.
	www-users.cs.york.ac.uk /~susan/cyc/m/mersenne.htm (192 words)

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