1. Mersenne Prime - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/mersenne_prime . Categories Articles containing proofs Classes of prime numbers http://en.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 As of August 2007 , only 44 Mersenne primes are known; the largest known prime number (2 −1) is a Mersenne prime and in modern times the largest known prime has nearly always been a Mersenne prime. Like several previous Mersenne primes, it was discovered by a distributed computing project on the Internet, known as the Great Internet Mersenne Prime Search (GIMPS). Contents About Mersenne primes Searching for Mersenne primes Theorems about Mersenne numbers History ... edit About Mersenne primes Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether there is a largest Mersenne prime, which would mean that 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 order of growth . It is also not known whether infinitely many Mersenne numbers with prime exponents are composite , although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes A basic theorem about Mersenne numbers states that in order for M n to be a Mersenne prime, the exponent

2. Mersenne Prime - Wikipedia Mersenne prime. A Mersenne prime is a prime number that is one less than a power of two. For example, 3 = 41 = 22-1 is a Mersenne prime. http://www.wikipedia.ws/wikipedia/me/Mersenne_prime.html

Contents Mersenne prime A Mersenne prime is a prime number that is one less than a power of two. For example, 3 = 4-1 = 2 -1 is a Mersenne prime. So is 7 = 8-1 = 2 -1. But 15 = 16-1 = 2 -1 is not a prime. Fast algorithms for finding Mersenne primes are available, and this is why the largest known prime numbers today are Mersenne primes. Mersenne primes have a deep 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. 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 -1 is used. The calculation a a a a b a ab 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;

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4. The Nightstar Zoo :: View Topic - [3/8] "Danger" mersenne_prime. Monkey House Exhibit. Joined 16 Sep 2003. Total posts 524. Location UrbanaChampaign, Illinois. Gender Unknown http://zoo.nightstar.net/viewtopic.php?p=130331&sid=82e8fcafb4a2954ac359c597d164

5. Mersenne Prime - Simple English Wikipedia, The Free Encyclopedia This short article can be made longer. You can help Wikipedia by adding to it. Retrieved from http//simple.wikipedia.org/wiki/mersenne_prime http://simple.wikipedia.org/wiki/Mersenne_prime

Mersenne prime From the Simple English Wikipedia, the free encyclopedia that anyone can change 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 . For this it is necessary, 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

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

TYPES OF NUMBER MATHEMATICS 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 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. As time went on, larger and larger computers found many more Mersennes and, for a while the search belonged exclusively to those with the fastest computers. This changed in 1995 when the American computer scientist George Woltman began the Great Internet Mersenne Prime Search (GIMPS) by providing a database of what exponents had been checked, an efficient program based on the Lucas-Lehmer test that could check these numbers, and a way of reserving exponents to minimize the duplication of effort. Today GIMPS pools the combined efforts of dozens of experts and thousands of amateurs. This coordination has yielded several important results, including the discovery of the Mersennes

7. 2006-05-18 Wikipedia/Álvaro_Obregón 17 July 1928 1 December 1920 1 mersenne_prime. name. Primorial_prime. name. Twin_prime. name. Perfect_number mersenne_prime. name. Lucky_prime. name. Centered_triangular_number http://www.alvis.info/alvis_docs/wp_18052006/266.xml.gz

8. Mersenne Primes (#4): The Lucas-Lehmer Test « Bruce H. McCosar ((s*s) 2) % mersenne_prime if s 0 return True else return False def mersenne(limit) Returns a list of Mersenne Primes up to a given limit. http://bmccosar.wordpress.com/2007/05/21/mersenne-primes-4-the-lucas-lehmer-test

@import url( http://s.wordpress.com/wp-content/themes/pub/ocadia/style.css?m=1204782896 ); var gaJsHost = (("https:" == document.location.protocol) ? "https://ssl." : "http://www."); document.write(unescape("%3Cscript src='" + gaJsHost + "google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E")); Bruce H. McCosar Mersenne primes (#4): the Lucas-Lehmer test Posted in python at 6:31 pm by bmccosar In my previous article Mersenne prime . Going any farther beyond the region of 10^20 would seem impossible with this simple algorithm; I needed a better one. Version 4 of this mersenne.py the Lucas-Lehmer test mersenne.py (version 4): What is hard for me to believe is how hardy Python is. The real beauty of this demonstration is not finding the next few primes, but watching this program reliably and accurately $ time ./mersenne4.py Start: Mon May 21 19:09:57 2007 [3, 7, 31, 127, 8191, 131071, 524287, 2147483647L, 2305843009213693951L, 618970019642690137449562111L, 162259276829213363391578010288127L, 170141183460469231731687303715884105727L, 686479766013060971498190079908139321726943530014330540939446 345918554318339765605212255964066145455497729631139148085803 7121987999716643812574028291115057151L, 531137992816767098689588206552468627329593117727031923199444 138200403559860852242739162502265229285668889329486246501015 346579337652707239409519978766587351943831270835393219031728 127L] Finish: Mon May 21 19:09:58 2007 real 0m0.68 user 0m0.62 sys 0m0.009s 180 orders of magnitude further along the number line

9. List Perfect Numbers(C++) [Archive] - Ubuntu Forums (http//en.wikipedia.org/wiki/mersenne_prime) Yes, you are correct; in the time between posts I looked at the wiki article more closely and I changed my http://ubuntuforums.org/archive/index.php/t-498366.html

Ubuntu Forums The Ubuntu Forum Community Other Community Discussions Programming Talk ... PDA View Full Version : List Perfect Numbers(C++) navneeth July 11th, 2007, 10:43 AM This is an utterly simple program, but for some reason unknown to me, this does not work properly. //This program lists all the perfect numbers less than a given positive integer(user input) using namespace std; int n,m,i,sum=1; cout << "List all the perfect numbers less than: "; if(n%i == 0) sum += i; if(sum == n) I use the GNU g++ compiler v4.1.2. It compiles fine, but when I execute and give the input, I get the back shell prompt. I must add that the second for loop works(i.e., when I test if a given number is perfect or not, or in other words, a fixed n), but that's not what I want here. Thanks for any help. GeneralZod July 11th, 2007, 10:56 AM Is m being read in correctly? Should "sum" not be reset to 1 for each n? July 11th, 2007, 11:57 AM here is mine: //This program lists all the perfect numbers less than a given positive integer(user input) int main (int argc, char **argv)

10. MathLinks :: View Topic - 2^n-1 http//en.wikipedia.org/wiki/mersenne_prime You are looking for mersenne primes. Post Posted. ProfilePMEmail. azjps Poincare Conjecture Offline http://www.mathlinks.ro/viewtopic.php?t=183939

11. Id:A098814 - OEIS Search Results A098814, Least k such that k*mersenne_prime(n) 1 and k*mersenne_prime(n) + 1 are twin primes. +0 1. 2, 6, 42, 144, 72, 312, 144, 234, 1512, 672, 2226, http://www.research.att.com/~njas/sequences/A098814

Greetings from The On-Line Encyclopedia of Integer Sequences Hints Search: id:A098814 Displaying 1-1 of 1 results found. page 1 short internal text references ... off Least k such that k*Mersenne_prime(n) - 1 and k*Mersenne_prime(n) + 1 are twin primes. list graph listen OFFSET CROSSREFS Sequence in context: Adjacent sequences: KEYWORD nonn AUTHOR Pierre CAMI (pierrecami(AT)tele2.fr), Oct 07 2004 page 1 Search completed in 0.002 seconds Lookup Welcome Find friends Music ... Superseeker Maintained by N. J. A. Sloane njas@research.att.com Last modified March 31 03:19 EDT 2008. Contains 137767 sequences. Legal Notice

12. SfR Fresh: [dmalloc-5.4.2.tgz] Member Dmalloc_rand.c (dmalloc-5.4.2/dmalloc_ ... include dmalloc_rand.h define MAGIC_A 16807 /* magic number */ define mersenne_prime 2147483647UL /* mersenne prime 2^31 1 */ define MAGIC_QUOTIENT http://www.sfr-fresh.com/unix/misc/dmalloc-5.4.2.tgz:a/dmalloc-5.4.2/dmalloc_ran

SfR Fresh " - the SfR Freeware/Shareware Archive Member "dmalloc-5.4.2/dmalloc_rand.c" of archive dmalloc-5.4.2.tgz As a special service "SfR Fresh" has tried to format the requested source page into HTML format using (guessed) C and C++ source code syntax highlighting with prefixed line numbers. Alternatively you can here view or download the uninterpreted source code file. That can be also achieved for any archive member file by clicking within an archive contents listing on the first character of the file(path) respectively on the according byte size field. * Internal random number generator * This file is part of the dmalloc package. * Permission to use, copy, modify, and distribute this software for * any purpose and without fee is hereby granted, provided that the * copies, and that the name of Gray Watson not be used in advertising * or publicity pertaining to distribution of the document or software * without specific, written prior permission. * Gray Watson makes no representations about the suitability of the * software described herein for any purpose. It is provided "as is"

13. Mersenne Prime - Overclocking Wiki Retrieved from http//www.overclockingwiki.org/wiki/index.php?title=mersenne_prime . Category Category needed. Views. Article; Discussion; View source http://www.overclockingwiki.org/wiki/index.php?title=Mersenne_prime

14. Mersenne Prime - Indopedia, The Indological Knowledgebase Retrieved from http//indopedia.org/mersenne_prime.html . This page has been accessed 606 times. This page was last modified 0125, 2 Dec 2004 by Indopedia http://indopedia.org/Mersenne_prime.html

Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch Categories Number theory Printable version ... Wikipedia Article Mersenne prime ज्ञानकोश: - The Indological Knowledgebase 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;

15. CastleCops® HT Log: Problem Is 'Search Results' At Startup C\Documents and Settings\Owner\Desktop\mersenne_prime\PRIME95.EXE c\Program Files\Norton AntiVirus\SAVScan.exe C\WINDOWS\System32\svchost.exe http://www.castlecops.com/t111689-HT_log_problem_is_Search_Results_at_startup.ht

About CastleCops Become Premium Our Sponsors CastleCops CastleCops Blog CastleCops Deutsch CastleCops Hashes CastleCops Mirrors CastleCops Wiki PIRT Squad How did I get infected? Unknown file uploads UDRP R3 URL SearchHook O2/O3 BHOs/Toolbars O4 Startups O9 Internet Explorer Buttons O10 LSPs O16 ActiveX O18 Protocol Hijackers O21 ShellServiceObjectDelayLoad O22 Shared Task Scheduler O23 XP/NT Services Need help ? Click here to register for free! Absolutely zero advertisements on this site $8155.22 of $21422.68 Help CastleCops serve the community on new servers, Donate Here to reach our goal. Donation/Premium Donations . Become Premium Today! Security Central Home PIRT/Fried Phish MIRT SIRT ... Acceptable Use Policy Survey Was 2007 a good year? Yes it was a wonderful year Yes, but there is always room for improvement Status quo It was a challenge Other (leave comment) Results Polls Votes: Comments: Forum FAQ Search Usergroups Profile Login to check your private messages Login Select FavForums HT log: problem is 'Search Results' at startup All FavForums Trend Micro HijackThis Logs ... View next topic Author Message Cadet Joined: Mar 16, 2005

16. Mersenne Prime - CryptoDox Retrieved from http//www.cryptodox.com/mersenne_prime . Categories Prime numbers Articles containing proofs. Article; Discussion; View source; History http://cryptodox.com/Mersenne_prime

Log in / create account Navigation Main Page Community portal Current events Recent changes ... Project Wonderful - Your ad here, right now, for as low as $0.00 Mersenne prime From CryptoDox, The Online Encyclopedia on Cryptography and Information Security Jump to: navigation search A Mersenne prime is a Mersenne number that is a prime number In mathematics , a Mersenne number is a number that is one less than a power of two M n n As of August 2007 , only 44 Mersenne primes are known; the largest known prime number (2 . Like several previous Mersenne primes, it was discovered by a distributed computing project on the Internet, known as the Great Internet Mersenne Prime Search (GIMPS). Contents About Mersenne primes Searching for Mersenne primes Theorems about Mersenne numbers History ... External links About Mersenne primes Many fundamental questions about Mersenne primes remain unresolved. It is not even known whether there is a largest Mersenne prime, which would mean that 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 order of growth . It is also not known whether infinitely many Mersenne numbers with prime exponents are composite , although this would follow from widely believed conjectures about prime numbers, for example, the infinitude of Sophie Germain primes A basic theorem about Mersenne numbers states that in order for M n to be a Mersenne prime, the exponent

17. PhysOrgForum Science, Physics And Technology Discussion Forums [Powered By Invis Of course the 44th Mersenne Prime Number is a most interesting one http//en.wikipedia.org/wiki/mersenne_prime. Posted by PIATLAS Feb 20 2008, 0429 AM http://www.physforum.com/index.php?act=Print&client=printer&f=20&t=20491

18. Mersenne Prime - Wikipedia Retrieved from http//nostalgia.wikipedia.org/wiki/mersenne_prime . This page was last modified 0443, 15 January 2005. Content is available under GNU Free http://nostalgia.wikipedia.org/wiki/Mersenne_prime

Mersenne prime From Wikipedia HomePage Recent changes View source Page history ... Log in Special pages Double redirects Broken redirects Disambiguation pages Log in Preferences My watchlist Recent changes Upload file File list Gallery of new files User list Statistics Random page Orphaned pages Uncategorized pages Uncategorized categories Uncategorized files Uncategorized templates Unused categories Unused files Wanted pages Wanted categories Most linked to pages Most linked to categories Most linked-to templates Pages with the most categories Most linked to files Pages with the most revisions Pages with the fewest revisions Short pages Long pages New pages Oldest pages Dead-end pages Protected pages Protected titles All pages Prefix index List of blocked IP addresses and usernames User contributions What links here Book sources Categories Export pages Version System messages Logs MIME search Search for duplicate files List redirects Unused templates Random redirect Pages without language links File path Search List of Wikimedia wikis Expand templates CategoryTree Gadgets Parser diff test Cross-namespace links Wikimedia Board of Trustees election Search web links Printable version Named after 17th century French mathematician Marin Mersenne , a Mersenne prime is a prime number that is one less than a power of two. For example, 3 = 4-1 = 2

19. Patterns In Prime Numbers “Mersenne Prime” http//en.wikipedia.org/wiki/mersenne_prime. Wiki, 2007. “Prime Number” http//en.wikipedia.org/wiki/Prime_number. Wiki, 2007. http://www.virtualsciencefair.org/2007/fras7j2/conclusion.htm

Prime Time Conclusion Bibliography All navigation bar images Clipart, 2007. http://en.wikipedia.org/wiki/Prime_number http://en.wikipedia.org/wiki/Fermat_Prime http://www.math.utah.edu/~pa/math/primelist.html http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Prime_numbers.html http://mathforum.org/dr.math/faq/faq.prime.num.html http://java.sun.com/docs/books/tutorial/ History of Prime Numbers Uses of Prime Numbers Patterns in Prime Numbers Types of Prime Numbers Prime Number Programs I Wrote Conclusion and Bibliography Take Me Home!

20. Wiki Mersenne Prime Wiki Mersenne prime. Contents 1. About Mersenne primes 2. Searching for Mersenne primes 3. Theorems about Mersenne numbers 4. History http://wapedia.mobi/en/Mersenne_prime

Wiki: Mersenne prime Contents: 1. About Mersenne primes 2. Searching for Mersenne primes 3. Theorems about Mersenne numbers 4. History ... 11. . 1. Math World Links In mathematics , a Mersenne number is a number that is one less than a power of two Home Licensing Wapedia: For Wikipedia on mobile phones

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