Factorization of the eighth Fermat number

61. R. P. Brent and J. M. Pollard, Factorization of the eighth Fermat number, Mathematics of Computation 36 (1981), 627-630. MR 83h:10014. Preliminary announcement in AMS Abstracts 1 (1980), 565, 80T-A212.

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We describe a Monte Carlo factorization algorithm which was used to factorize the Fermat number F8 = 2256 + 1. Previously, F8 was known to be composite, but its factors were unknown.


At the time of this paper, Lenstra's elliptic curve method (ECM) had not been invented. A modification [51] of Pollard's rho method was used to factor F8 and several Mersenne numbers.

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