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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Abstract
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.
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 F8 and several
Mersenne numbers.
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