81. Mersenne Primes One such form that has been explored a great deal is that of mersenne primes, namedfor marin mersenne, a French monk who began the study of these numbers in 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.

82. Mersenne.org Página Principale Translate this page Los primos de mersenne se llaman así debido al monje francés marinmersenne. En su tiempo, marin mersenne se comportó como un http://www.ctv.es/USERS/gbv/GIMPS/default.htm

www.mersenne.org George Woltman esta Los primos de Mersenne Marin Mersenne lo hace sencillo ... Cadenas de Cunningham Ayuda a encontrar factores de los "mas buscados" números compuestos. Paul Zimmermann ha fundado ECMNet NFSNet (number field sieve) . Concretamente, los de forma 2 N -1 and 2 N Ayuda a encontrar nuevos un factor de MM61 Seti@Home K-optimal lattice rules primos gemelos y la constante de Brun que puede usar tu ayuda. Un proyecto para encontrar sumas iguales de potencias CS-Cipher Distributed.net RC5 Cracking Effort y ECCp-97 web tiene una programa para hallar soluciones de este problema y similares. . A lo mejor ya han comenzado un nuevo proyecto. Fecha del texto original: 1 de Diciembre de 1999

83. IU Cook Music Library: A Bibliography Of Writings About The Bassoon, 17th-19th C Translated and edited by David Z. Crookes. Early Music Series, 7. OxfordClarendon Press, 1986. mersenne, marin. Harmonie universelle http://www.music.indiana.edu/musicref/bassoonp.htm

William and Gayle Cook Music Library A Bibliography of Writings about the Bassoon, 17th-19th Centuries: Primary Sources (in Chronological Order) Compiled by David Lasocki This bibliography was compiled for Proceedings of the International Double-Reed Symposium Utrecht 1994 (Utrecht: STIMU, 1997), ed. David Lasocki. We are grateful to STIMU for granting permission to load the bibliography on our web site. Praetorius, Michael. The Syntagma Musicum of Michael Praetorius. Volume Two: De Organographia, First and Second Parts. Syntagma Musicum, II: De Organographia, Parts I and II. Translated and edited by David Z. Crookes. Early Music Series, 7. Oxford: Clarendon Press, 1986. Mersenne, Marin. Harmonie Universelle: The Books on Instruments. Translated by Roger E. Chapman . The Hague: Martinus Nijhoff, 1957. Celle: Moeck, 1987. Trichet, Pierre. ca Speer, Daniel. Musica bellicosa ... and a Scale of the Gamut for the Bassoon. London: John Walsh, 1730. Majer, Joseph Friedrich Bernhard Caspar. Eisel, Johann Philipp.

84. Index Des Noms Commençant Par M Translate this page mersenne, Julienne ( - après 9 février 1700 72 - Oizé ?) mersenne, Louis ( - )mersenne, Louis ( - ) mersenne, Marie ( - ) mersenne, marin (20 avril 1617 72 http://www.chez.com/mremars/genealogie/ancetres/idx4d0.htm

85. Informations Généalogiques Translate this page Décès 2 janvier 1676 à 72 - Yvré-le-Pôlin ! mersenne, Julienne, mersenne,marin, Sexe Masculin Naissance septembre 1650 à 72 - Oizé. http://www.chez.com/mremars/genealogie/ancetres/dat40.htm

86. BBC News | SCI/TECH | Number Takes Prime Position The man whose name they now bear, the French monk marin mersenne (15881648),made a famous prediction about which values of P would yield a prime. http://news.bbc.co.uk/hi/english/sci/tech/newsid_1693000/1693364.stm

CATEGORIES TV RADIO COMMUNICATE ... INDEX SEARCH You are in: Sci/Tech Front Page World UK ... AudioVideo SERVICES Daily E-mail News Ticker Mobiles/PDAs Feedback ... Low Graphics Wednesday, 5 December, 2001, 11:42 GMT Number takes prime position By BBC News Online science editor Dr David Whitehouse The largest prime number yet discovered has just been revealed to the world. There are more primes out there George Woltman, Gimps founder The new number, expressed as 2 -1, contains 4,053,946 digits and would take the best part of three weeks to write out longhand. 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 Gimps project spent 13,000 years of computer time to find the new prime number. Big effort Cameron used an 800 MHz AMD T-Bird PC, running part-time for 45 days to find the number.

87. életrajzok: M mersenne, marin (1588. szeptember 8.—1648. szeptember 1.) francia matematikus,minorita szerzetes. METÓN (Kr. e. 430k.) athéni csillagász és geométer. http://www.iif.hu/~visontay/ponticulus/eletrajzok/m.html

rovatok j¡t©k arch­vum jegyzetek mutat³k kitekintő v©lem©nyek inform¡ci³k ©letrajzok magyar¡zatok forr¡sok MACLAURIN, Colin (1698. febru¡r ?—1746. janu¡r 14.): sk³t matematikus. P¡lyafut¡s¡t csodagyerekk©nt kezdte: 11 ©vesen ©retts©gizett, 15 ©vesen magiszteri fokozatot szerzett, 19 ©vesen m¡r a aberdeeni Marishal College matematika tansz©k©nek vezetője. Első munk¡j¡t 21 ©ves kor¡ban publik¡lta. C­me Rendszeres geometria volt ©s fontos algebrai geometriai eredm©nyeket tartalmazott. Egy k©sőbbi munk¡j¡ban NEWTON fluxi³elm©let©t fejlesztette tov¡bb. Ebben a műben szerepelt a Maclaurin-sor is, amely a Taylor-sor speci¡lis esete. MAGYARORSZGI GY–RGY Mester (Georgius de Hungaria) (?, 1422?—R³ma, 1502): magyar matematikus. Ő ­rta 1499-ben az első, magyar szerzőtől sz¡rmaz³ matematikai művet. ‰let©ről keveset tudunk. Val³sz­nűleg a pozsonyi egyetem di¡kja volt. M©g di¡k kor¡ban elhurcolt¡k a t¶r¶k¶k. Harminc ©vi rabs¡g ut¡n t©rt haza. Domonkosrendi szerzetes lett ©s a hollandiai Utrecht k¶zel©ben telepedett le. Sz¡mol³mesterk©nt is műk¶d¶tt. Latin nyelven jelent meg a Magyarorsz¡gi Gy¶rgy Mester (Georgius de Hungaria) aritmetik¡j¡nak foglalata h¡rom r©szben c­mű műve. A 20 oldalas k¶nyvecsk©t, mint ősnyomtatv¡nyt 1965-ben ºjra kiadt¡k Hollandi¡ban.

88. Club-Internet Encyclopédie Translate this page un ami, Titres (1-1 / 1) mersenne (marin), marin mersenne Tous lesmots sont cliquables Thèmes associés Voir aussi Philosophe http://www.club-internet.fr/cgi-bin/h?Mersenne

89. TecaLibri: Marin Mersenne: Opere http://tecalibri.altervista.org/M/MERSENNE-M_OPE.htm

TecaLibri Marin Mersenne: opere Nasce l'8 settembre, a Oizé. 1623 Quaestiones celeberrimae in Genesim 1624 L'impiété des déistes 1624 Questions inouyes ou Récreation des Sçavants, Paris 1625 La verité des sciences, Paris 1626 Synopsis mathematica 1636 Harmonie Universelle, Paris, [ rif. 1644 Cogitata physico-mathematica. In quibus tan naturae quàm artis effectus admirandi certissimi demonstrationibus explicantur, Sumptibus Antonij Bertier, Paris, [ rif. Muore il 1 settembre, a Parigi.

90. TecaLibri: Marin Mersenne: Opere 1624 Questions inouyes ou Récreation des Sçavants, Paris; http://web.infinito.it/utenti/t/tecalibri/M/MERSENNE_OPE.htm

TecaLibri Marin Mersenne: opere Nasce. 1624 L'impiété des déistes 1624 Questions inouyes ou Récreation des Sçavants, Paris 1625 La verité des sciences, Paris 1636 Harmonie Universelle, Paris, [ rif. Muore.

91. The Prime Page's Links++: Theory/special_forms/Mersenne Luke's marin mersenne Page Images, sounds, references, links, mailing listand software. An eclectic collection to warm any mersenne lover's heart. http://primes.utm.edu/links/theory/special_forms/Mersenne/

Links related to Prime Numbers Add Update New Popular The Mersenne primes are primes of the form 2 p -1 where p is a prime number. These are usually the largest known prime and are certainly the most studied. Below are links to pages containing information on these important primes. Top theory special forms : Mersenne Next 10 of 11 links Resources in theory : special forms : Mersenne A search for a factor of 2^(2^61-1)-1 - An organized search for a factor of this double Mersenne number. Theory, free software, and status. (Added: 28-Dec-2001 Hits: 190 Rating: Votes: 0) Rate It Ars Technica Team Prime Rib - A GIMPS team dedicated to finding Mersenne primes... (Added: 14-Sep-2001 Hits: 124 Rating: 10.00 Votes: 8) Rate It Conrad Curry's Mersenne Prime Freeware - Links to programs for finding Mersenne primes and packages for large integer arithmetic. (Added: 5-Aug-2000 Hits: 401 Rating: Votes: 0) Rate It Double-Mersenne search status - Status of the serach for factors of M(M(p)) where M(p) is the Mersenne prime with exponent p. (Added: 28-Dec-2001 Hits: 109 Rating: 2.00 Votes: 1)

92. Nombre Premier De Mersenne - Wikipedia Translate this page est un nombre premier s'écrivant sous la forme 2 p - 1. Ces nombres premiers doiventleur nom à un mathématicien français du XVIIe siècle, marin mersenne. http://fr.wikipedia.org/wiki/nombre_premier_de_Mersenne

Accueil Modifications récentes Modifier cette page Historique Pages spéciales Préférences Liste de suivi Modifications récentes Copier un fichier Liste des images Liste des participants Statistiques Une page au hasard Pages orphelines Images orphelines Les plus populaires Les plus demandées Articles courts Articles longs Nouvelles pages Toutes les pages Adresses IP bloquées Page de Maintenance Librairies en ligne Version imprimable Discuter Identification Aide Autres langues: English Nombre premier de Mersenne Un article de Wikipédia, l'encyclopédie libre. Un nombre premier de Mersenne est un nombre premier s'écrivant sous la forme 2 p - 1. Ces nombres premiers doivent leur nom à un mathématicien français du XVIIe siècle Marin Mersenne Les premiers nombres premiers de Mersenne sont: 3, 7, 31, 127. Au 24 octobre 2002, seulement 39 nombres premiers de Mersenne ont été découverts et vérifiés. Les nombres premiers de Mersenne sont en connexion avec les nombres parfaits , qui sont les nombres égaux à la somme de leurs diviseurs propres. C'est cette connexion qui a motivé historiquement l'étude des nombres premiers de Mersenne. Dès le IVe siècle av. J.-C.

93. Untitled Notable mathematicians who revived the activity in Number theory in this period areFather marin mersenne (15881648), Pierre de Fermat (1601-1665), Leonhard http://www.math.ucla.edu/~hida/106.1.02f/Hist3.html

Historical Note 3 Renaissance of Number Theory Marin Mersenne Marin Mersenne had a great interest in learning from intellectuals at the time and was an able physicist and mathematician (and Jesuit-educated friar). He started organizing a regular meeting of mathematicians at his monastery. He also wrote many letters to his fellow mathematicians, which plays a role of scientific journals at present day in publicizing theorems newly proven and problems newly solved. Although he did not make much contributions in creating new knowledge, he had capacity of understanding new ideas coming out of creative mathematicians who participated in his gathering. In this sense, he contributed to the advancement of knowledge offering a place of discussing Mathematics and Science to those who can make Scientific research. His main contribution to Number Theory is: Study of Mersenne primes: prime numbers of the form 2^n-1. If this type of number is a prime, we call this number M(n) This is related to the study of perfect numbers. By the perfect number formula of Euclid (text page 461, and historical note 2), 2^( p M(p) is a perfect number. Later Euler proved that all even perfect numbers are in such a form. Mersenne knew that

94. Mersenne Prime Search An organized search for mersenne prime numbers. Free software provided.Category Science Math Number Theory Prime Numbers mersenne...... GIMPS uses the LucasLehmer primality test which takes advantage of the specialproperties of mersenne numbers. 39th Known mersenne Prime Found!! http://www.mersenne.org/prime.htm

GIMPS Home Page NEW! Version 22! GIMPS Forums! Pages available in Danish Dutch French German ... Polish , and Spanish . Warning: These translations may not be up-to-date - use AltaVista as necessary. Recent News 62722^131072 + 1 prime. At 628,808 digits this is the 5th largest known prime number. This moves GIMPS first prime discovery, M1398269, into 6th place. Now I must change the banner of every mersenne.org web page! Congratulations to discoverer Michael Angel and to Yves Gallot who wrote the program that discovered this generalized Fermat prime. M6972593 is the 38th Mersenne prime. GIMPS has finished testing and double-checking all Mersenne numbers below M6972593. This proves there are no smaller undiscovered Mersenne primes. Version 22 released. Although not a required upgrade, this new version has many small improvements over version 21. The download page has the full details. GIMPS forums. Here you can chat with fellow GIMPS members, get help with installation questions, learn more about how GIMPS works, etc. 39th Known Mersenne Prime Found!!

95. Elementary Number Theory - Kenneth H. Rosen Primes History, Theorems, and Lists) Biographical information about marin Mersennecan be found at the MacTutor History of Mathematics Archive at http//www http://www.aw.com/rosen/resourcesc_7.html

Annotated Web Links CHAPTER 7 Multiplicative Functions Return to Annotated Web Links Home 7.1 The Euler's Phi-Function Page 230 Biographical information about Joseph Liouville can be found at the MacTutor History of Mathematics Archive at http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Liouville.html (Liouville) 7.2 The Sum and Number of Divisors Page 236 Biographical information about Srinivasa Ramanujan can be found at the MacTutor History of Mathematics Archive at http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Ramanujan.html (Ramanujan) 7.3 Perfect Numbers and Mersenne Primes Page 239 A survey article about perfect numbers can be found at the St. Andrews History of Mathematics site at http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Perfect_numbers.html (Perfect Numbers) Page 241 A wealth of information about Mersenne primes can be found at http://www.utm.edu/research/primes/mersenne.shtml

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