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.
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Fermat numbers, named after the French mathematician Pierre de Fermat, are numbers of the form Fn= 22n+1, where n is some non-negative integer.
The first few Fermat numbers are F0=3, F1=5, F2=17, F3=257, F4=65537 and F5=4294967297 and were computed by Fermat himself, who claimed that they were all prime numbers. On this basis, he conjectured that the Fermat numbers were always prime but this turned out to be false. The Swiss mathematician Leonhard Euler showed that F5 was divisible by 641 and therefore not prime, contrary to what Fermat had claimed.
To date, no other Fermat number was found to be prime and it is known that all Fermat numbers Fn with n between 5 and 30 (and several other values of n) are composite. The current guess is that no other Fermat number beyond the first five, is prime.
A test devised by Pepin in 1877 allows the primality of a Fermat number to be tested relatively quickly on a computer, even though these numbers get huge very quickly. However, Pepin's test does not give the factors of a Fermat number when it is composite and it remains a challenge to factor the larger composite Fermat numbers.