## 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.
Abstract:
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Paper:
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## Abstract

We describe a Monte Carlo factorization algorithm which was used to factorize
the Fermat number
F_{8} = 2^{256} + 1.
Previously, F_{8} was known to be
composite, but its factors were unknown.
## Comments

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 F_{8} and several
Mersenne numbers.
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