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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Factorization of the tenth Fermat number


Author: Richard P. Brent
Journal: Math. Comp. 68 (1999), 429-451
MSC (1991): Primary 11Y05, 11B83, 11Y55; Secondary 11--04, 11A51, 11Y11, 11Y16, 14H52, 65Y10, 68Q25
MathSciNet review: 1489968
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Abstract: We describe the complete factorization of the tenth Fermat number $F_{10}$ by the elliptic curve method (ECM). $F_{10}$ is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The 40-digit factor was found after about 140 Mflop-years of computation. We also discuss the complete factorization of other Fermat numbers by ECM, and summarize the factorizations of $F_5, \dots, F_{11}$.


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Additional Information

Richard P. Brent
Affiliation: Oxford University Computing Laboratory, Wolfson Building, Parks Road, Oxford, OX1 3QD, United Kingdom

DOI: http://dx.doi.org/10.1090/S0025-5718-99-00992-8
PII: S 0025-5718(99)00992-8
Keywords: Computational number theory, Cunningham project, ECM, elliptic curve method, factorization, Fermat number, $F_9$, $F_{10}$, $F_{11}$, integer factorization
Received by editor(s): February 2, 1996
Received by editor(s) in revised form: May 20, 1997
Article copyright: © Copyright 1999 American Mathematical Society