Art of Computer Programming, Volume 2: Seminumerical Algorithms, Third Edition by Donald E. Knuth

Author:Donald E. Knuth [Knuth, Donald E.]
Language: eng
Format: epub, pdf
Publisher: Addison-Wesley Professional
Published: 1998-05-29T22:00:00+00:00

was found by the number field sieve, after four months of computation that occupied otherwise idle time on about 700 workstations [Lenstra, Lenstra, Manasse, and Pollard, Math. Comp. 61 (1993), 319–349; 64 (1995), 1357]; here p99 denotes a 99-digit prime number. The next Fermat number has twice as many digits, but it yielded to the elliptic curve method on October 20, 1995:

[Richard Brent, Math. Comp. 68 (1999), 429–451.] In fact, Brent had already used the elliptic curve method to resolve the next case as early as 1988:

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