The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
All other sections in this Literature Study Guide are owned and copyrighted by BookRags, Inc.
Mersenne numbers are numbers of the form 2p-1 where p is a prime number. If the Mersenne number 2p-1 itself is prime then it is called a Mersenne prime. The first few are 22-1= 3, 23-1 = 7, 25-1= 31, 27-1 = 127 are all prime numbers but the next one, 211-1 = 2047 is divisible by 23 and therefore is not prime.
Although Mersenne primes have been considered since antiquity because of their relation with perfect numbers, they are named after the French clergyman, Father Marin Mersenne, who, in 1644, made a list (with some errors) of the Mersenne primes with exponent p at most 257.
Most Mersenne numbers are not prime and, to date, 38 Mersenne primes have been discovered out of the more than 400,000 Mersenne numbers tested. It is believed, but not known for sure, that there exists infinitely many Mersenne primes. The largest known Mersenne prime is 26972593-1, a number of more than two million digits, which was discovered by N. Hajratwala, G. Woltman and S. Kurowski who are all amateur mathematicians from the United States. It was found as part of the Great International Mersenne prime search, which is a worldwide effort to use idle time on home computers to find Mersenne primes and has led to advances in distributed computing. They use an implementation by G. Woltman of a test devised by the French mathematician E. Lucas and improved by the American mathematician D. N. Lehmer specifically to test the primality of Mersenne numbers.