Factorization of the tenth and eleventh Fermat numbers

Factorization of the tenth and eleventh Fermat numbers (1996)

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by Richard P. Brent

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Datum	Value	Source
TITLE	Factorization of the tenth and eleventh Fermat numbers	INFERENCE
AUTHOR NAME	Richard P. Brent	user correction
AUTHOR AFFIL	Department of Computer Science; Faculty of Engineering and Information Technology; Computer Sciences Laboratory; Research School of Information Sciences and Engineering; and the; Department of Computer Science; Faculty of Engineering and Information Tec	user correction
AUTHOR ADDR	Canberra ACT 0200; Australia	user correction
ABSTRACT	. We describe the complete factorization of the tenth and eleventh Fermat numbers. The tenth Fermat number is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The eleventh Fermat number is a product of five prime factors with 6, 6, 21, 22 and 564 decimal digits. We also note a new 27-decimal digit factor of the thirteenth Fermat number. This number has four known prime factors and a 2391-decimal digit composite factor. All the new factors reported here were found by the elliptic curve method (ECM). The 40-digit factor of the tenth Fermat number was found after about 140 Mflop-years of computation. We discuss aspects of the practical implementation of ECM, including the use of special-purpose hardware, and note several other large factors found recently by ECM. 1. Introduction For a nonnegative integer n, the n-th Fermat number is F n = 2 2 n + 1. It is known that F n is prime for 0 n 4, and composite for 5 n 23. Also, for n 2, the factors of F n are of th...	user correction - Legacy Corrections
YEAR	1996	INFERENCE
VENUE TYPE	TECHREPORT	INFERENCE
TECH	Report TR-CS96 -02	INFERENCE
CITATIONS	84 found	ParsCit 1.0