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Word-of-the-Day: Mersenne prime

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Fri, 28 Dec 2001 15:12:42 -0800

THE WHATIS.COM WORD-OF-THE-DAY   
December 28, 2001

Mersenne prime
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TODAY'S WORD: Mersenne prime

See our definition with hyperlinks at
http://whatis.techtarget.com/definition/0,,sid9_gci788348,00.html

A Mersenne (also spelled Marsenne) prime is a specific type of prime
number. It must be reducible to the form 2n - 1, where n is a prime
number. The term comes from the surname of a French monk who first
defined it. 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. 

With the advent of computers to perform number-crunching tasks
formerly done by humans, ever-larger Mersenne primes (and primes in
general) have been found. The quest to find prime numbers is akin to
other numerical searches done by computers. Examples are the decimal
expansions of irrational numbers such as pi (the
circumference-to-diameter ratio of a circle) or e (the natural
logarithm base). 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. For this reason, Mersenne primes
are of particular interest to developers of strong encryption
methods. 

RELATED TERMS:

prime number
http://whatis.techtarget.com/definition/0,,sid9_gci284011,00.html

irrational number
http://whatis.techtarget.com/definition/0,,sid9_gci283983,00.html

encryption 
http://searchsecurity.techtarget.com/sDefinition/0,,sid14_gci212062,00.html
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SELECTED LINKS

Chris Caldwell discusses the history of Mersenne primes and provide
links to more information. 
http://primes.utm.edu/glossary/page.php/Mersennes.html
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