61. MathWorld News: 42nd Mersenne Prime (Probably) Discovered MathWorld Headline News 42nd Mersenne Prime (Probably) Discovered By Eric W. Weisstein. February 18, 2005Less than a year after the 41st Mersenne prime was reported http://www.lehigh.edu/~bad0/bdNews42ndMers3.html

MathWorld Headline News 42nd Mersenne Prime (Probably) Discovered By Eric W. Weisstein February 18, 2005Less than a year after the 41st Mersenne prime was reported ( MathWorld headline news: June 1, 2004 ), Great Internet Mersenne Prime Search (GIMPS) project organizer George Woltman is reporting in a Feb. 18 email to the GIMPS mailing list that a new Mersenne number has been flagged as prime and reported to the project's server. If verified, this would be the known Mersenne prime, as well as the largest prime number known of any kind. Mersenne numbers are numbers of the form M n n - 1, giving the first few as 1, 3, 7, 15, .... Interestingly, [by] the definition of these numbers the n th Mersenne number is simply a string of n 1s when represented in binary . For example, M is a Mersenne number. In fact, since 127 is also prime, 127 is also a Mersenne prime. [** But notice that 2 -1=(23)(89) is not prime. **] The study of such numbers has a long and interesting history, and the search for Mersenne numbers that are prime has been a computationally challenging exercise requiring the world's fastest computers. Mersenne primes are intimately connected with so-called perfect numbers , which were extensively studied by the ancient Greeks, including by Euclid. A complete list of

62. Redirection et al. on the Great Internet Mersenne Prime Search (GIMPS) volunteer network and then verified by T. Reix, J. Gilchrist, and G. Ballester Valor. http://www.perfsci.com/souvenirs.htm

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63. Notable Properties Of Specific Numbers (page 9) At MROB If a Mersenne number is prime (as is the case for 127) it is called a Mersenne prime. Here is a list of all known Mersenne primes. http://mrob.com/pub/math/numbers-9.html

mrob Numbers Largenum Sequences ... Core Values Search: Notable Properties of Specific Numbers First page Back to page 8 Forward to page 10 Last page (page 25) oblong numbers because they correspond to the area of an "oblong" rectangle whose length is one greater than its width. They are also called promic numbers; each is twice a triangular number. The sequence of oblong numbers starts: , ... (Sloane's ; my ) See also , and For any whole number n , compute the square root of e n and round up. For n =0, 1, 2, 3, ... through n =8 you get Fibonacci numbers n =9 you get 91, not the Fibonacci number . This is even a little more surprising to those who know that the Fibonacci sequence is an exponential sequence. (See also Amateur mathematicians fall into this sort of trap all the time, and it frequently ensnares even the most professional and experienced. It is now known as "Guy's Strong Law of Small Numbers There aren't enough small numbers to meet the many demands made of them. - Richard K. Guy In other words, if you encounter a small number in two different phenomena, don't assume any actual cause-and-effect relationship between the two unless you already know (or can prove) that there is one. Guy's paper gives many examples of possible coincidences involving small numbers, presenting them as questions to answer "yes" or "no". His example 29 also mentions the number 91:

64. The Great Internet Mersenne Prime Search 'The Great Internet Mersenne Prime Search' Paper by Patrick Kellogg http://www.patrickkellogg.com/school/papers/gimps.htm

Return to the home page for Patrick Kellogg The Great Internet Mersenne Prime Search The “Great Internet Mersenne Prime Search” is a large distributed computing project sponsored by the Mersenne organization at: http://www.mersenne.org/prime.htm . It was started by George Woltman in 1994 to find Mersenne primes, and in the last six years the group has found the four largest ones currently known. In addition to GIMPS, they also sponsor several other distribute mathematical projects at (http://www.mersenne.org/). Why would anyone want to try to find the next Mersenne prime? Well, besides the altruistic idea of contributing to scientific knowledge, the Electronic Frontier Foundation ( www.eff.org ) is offering a $100,000 reward to the first person that helps to discover a ten million digit (or higher) prime number. There are some caveats… $25,000 goes to charity and $20,000 to GIMPS, but it still leaves $55,000 for the lucky computer user. And the 1 in 250,000 odds are better than most state lotteries. Installation of the GIMPS software is easy. Different versions are available for Microsoft Windows 95/98 and NT/2000 (as well as the earlier 3.1), Linux, FreeBSD, OS/2 and DOS. Also, optimized code is available for different platforms, including PowerPC, StrongARM, UNIX, and older x86 machines. Though the software does not support multiple processors or multiple machines working on the same problem, they have a very robust server at “PrimeNet” (

65. Historical Timeline - April 6, 1972 1973 1975 1976 1977 1978 1979 File Format PDF/Adobe Acrobat Quick View http://www.cray.com/Assets/PDF/about/CrayTimeline.pdf

66. IEEE Xplore - Trace Representation Of Legendre Sequences Of by JS No 2002 - Cited by 38 - Related articles http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=556617

67. UCLA Find New Prime Number: 46th Mersenne Prime Discovered Using GIMP Search Mathematicians at the University of California in Los Angeles (UCLA) were celebrating last night after discovering a new 13 million digit Mersenne Prime Number. http://www.suite101.com/content/ucla-find-new-prime-number-a70749

68. NumberADay: September 2008 A Mersenne prime has the form 2p – 1, where p is a prime number. The 46th Mersenne prime is the first prime to be discovered out of order since Walt http://maanumberaday.blogspot.com/2008_09_01_archive.html

skip to main skip to sidebar Tuesday, September 30, 2008 x 17. is the smallest number (except 1) such that the sum of the cubes of the digits of the sum of the cubes of its digits equals itself: 1 = 244 and 2 is a refactorable number (divisible by the count of its divisors); it has a total of 8 divisors (1, 2, 4, 8, 17, 34, 68, ), with 8 among them. is a triangular number , which can be represented in the form of a triangular grid of points, where the first row contains a single element and each subsequent row contains one more element than the previous one. Hence, it is the sum of the first 16 positive integers. A representation of the first few triangular numbers. is 10001000 in base 2 (binary) and 88 in base 16. has a representation as a sum of two squares: Austria is an asteroid discovered in 1874. Sources: Number Gossip Wikipedia Posted by MAA Blogs at 8:00 AM 0 comments Labels: triangular number Monday, September 29, 2008 is a perfect cube, 5 is the smallest cube that is also the sum of two squares in two different ways: is the hypotenuse of a primitive Pythagorean triple: Space Shuttle mission STS- was the final servicing mission to the Hubble Space Telescope.

69. Perfect Number - ONJava.com The Independent Source For Enterprise A Mersenne Prime Number is a special type of Mersenne number, in that it is also a prime number. The first few Mersenne primes (where k = 2, 3, 5, http://onjava.com/onjava/2002/08/28/wsdc.html

What do searching for extraterrestrials, curing cancer, and finding big prime numbers all have in common? These problems are all being attacked with grid computing, a a technique of breaking a large problem into small tasks that can be computed independently. While projects like Seti@home and The Greatest Internet Mersenne Prime Search have received plenty of press for using the Internet to distribute tasks to end users around the globe, grid computing also takes place in more controlled environments, such as research and financial settings. But it is by using the power of the Internet and the ability to discover and access idle processes on users' machines that grid computing (once called distributed computing ), can access massive numbers of machines and processes. What does all this have to do with Web services? The grid's principal tasks discovery and utilization of idle processes are best done over a ubiquitous protocol like HTTP. Although not tied to HTTP, Web services are effectively synonymous with HTTP and allow middleware components to be invoked using a verbose ASCII-formatted message. Web services provide a framework that is ideal for grid computing architectures. The Web services framework consists of UDDI for lookup and discovery, WSDL for service definition, and SOAP/HTTP for service invocation. In this article, this Web services framework will be applied to the problem of factorizing large numbers to check if they are prime. The problem must first be understood in terms of the mathematics behind it. This problem will then be conceptualized and remodeled in UML, and finally the problem implemented in a service-oriented manner that can easily be translated to a grid computing architecture for scalability and rapid solution of the complex problem.

70. Breakfast With Knuth From our previous contact about the 37th Mersenne prime he already knew I was Knuth specifies the frame color for the 38th Mersenne prime poster that http://scottkurowski.com/knuth/

71. Largest Known Prime And The Great Internet Mersenne Prime Search - Puzzled By T- Jul 29, 2010 Itzik talks about the largest known prime and the program that was used to find it. http://www.sqlmag.com/blogs/puzzled-by-t-sql/tabid/1023/entryid/12993/Largest-Kn

72. Mersenne Prime Definition Of Mersenne Prime In The Free Online Encyclopedia. Mersenne prime mər′sen prīm (mathematics) A Mersenne number that is also a prime number. http://encyclopedia2.thefreedictionary.com/Mersenne prime

73. Mersenne Prime Numbers Mersenne prime numbers have their own web site which is dedicated to a netwide search for Mersenne prime numbers and related tasks. http://www.math.utah.edu/~pa/math/mersenne.html

Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah Mersenne Prime Numbers Mersenne prime numbers are numbers of the form For m to be prime, p itself must be prime, but that is not sufficient. Indeed, at present only 43 Mersenne prime numbers are known. They are obtained by letting p Note that for example so that for p = 11 we do not obtain a prime number. 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. Fine print, your comments, more links, Peter Alfeld, PA1UM [06-Aug-1999]

74. 29. The 46th Mersenne Prime - TIME's Best Inventions Of 2008 - TIME A Mersenne number is a positive number that can be expressed in the form 2n1. A Mersenne prime is a Mersenne number that is, well, prime. Searching for higher and higher http://www.time.com/time/specials/packages/article/0,28804,1852747_1854195_18541

75. Lucas-Lehmer Test - Rosetta Code Oct 26, 2010 %Mersenne Prime, but because of the rounding error in calculating the .. The program was still running, but as the next Mersenne prime is http://rosettacode.org/wiki/Lucas-Lehmer_test

76. BBC News | SCI/TECH | Number Takes Prime Position The new Mersenne prime has been independently verified using three weeks of computer time on a 667 MHz Alpha workstation. It is the fifth, record prime found by the Gimps project http://news.bbc.co.uk/2/hi/science/nature/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.

77. Welcome To The Prime Numbers Formula Jul 2, 2009 The generating formula of the Mersenne prime numbers. GIMPS, the Great Internet Mersenne Prime Search, was formed in January 1996 to http://www.primenumbersformula.com/

Number of visitors Pay Per Click Advertising Counter NAAS (USA) Awarded A++ = Excellent Grade to article of prime numbers formula by Prof. S.M.R.Hashemi Moosavi Note You are just permitted to use these information with mentioning the reference www.primenumbersformula.com Take a look at new photo gallery Note : This formula is one of the on-to generating functions for the prime numbers that for every natural "m" it generates all the prime numbers (3,5,7,2,11,13,2,17,19, ...) The presented "H.M" functions by Discoverer (Prof. Seyyed Mohammad Reza Hashemi Moosavi) are 6 numbers that 4 functions are by Wilson's theorem and one of them by Euler's function( and one of them by functions and functions are discovered by discoverer (Prof.S.M.R.Hashemi Moosavi). The software of this function is produced. Note : In Year of 2007 ( AAAS ) " National Association Of Academies Of Science " (USA) Awarded an A++ = Excellent grade to prime numbers formula and its results by prof.S.M.R.Hashemi Moosavi. Note : The discovery of prime numbers formula and its results has been published under an article in journal of "

78. Mersenne Prime # Of Digits Calculator SetPriority is a Windows command line program that will allow you to view or change both the process priority and thread priority of a running program http://gilchrist.ca/jeff/MprimeDigits/index.html

Mersenne Prime # of Digits Calculator by Jeff Gilchrist This program will calculate the number of decimal digits in the specified Mersenne number 2^p-1. More information about Mersenne Primes can be found on the Mersenne Prime Search site. Note: For the Windows binaries you will need to install the included " vcredist_x86.exe Microsoft Visual C++ 2008 Redistributable Package if the mprimedigits application does not work when you load it. Screen Shots This software is freeware and can be freely distributed. Use at your own risk. I take no responsibility for anything that happens to your equipment. Download Click to download the latest version: Windows Binaries: MprimeDigits v1.1 (1881 KB) [SHA-1: Linux/Unix Source Code: MprimeDigits Source v1.1 (2 KB) [SHA-1: Recent History v1.1 (September 3, 2008) Fixed rounding errors reported by R. Gerbicz. Command line version now accepts multiple p values on the command line (ie: mprimedigits 32582657 25964951 Now displays formula used to calculate # of digits so people can better understand how to calculate it themselves if they wish. v1.0 (August 30, 2008)

79. NDA Technologies Inc. Home Our business is Nuclear Fuel Rod Scanners. Products and Services Links Studies Downloads Company Information. ©2007 NDA Technologies Incorporated. http://www.ndatech.com/

Our business is Nuclear Fuel Rod Scanners Products and Services Links Studies Downloads ... Company Information

80. Mersenne Prime Primes Minus Numbers Gimps Slowinski Number Mersenne Prime Primes Minus Numbers Gimps Slowinski Number Economy. http://www.economicexpert.com/a/Mersenne:prime.htm

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