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Factorization of the Tenth Fermat Number

Richard P. Brent
Mathematics of Computation
Vol. 68, No. 225 (Jan., 1999), pp. 429-451
Stable URL: http://www.jstor.org/stable/2585124
Page Count: 23
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Factorization of the Tenth Fermat Number
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Abstract

We describe the complete factorization of the tenth Fermat number F10 by the elliptic curve method (ECM). F10 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 F5,..., F11.

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