Factorization of F11

F11 = 2211 = 22048 + 1 is the 11-th Fermat number.

In 1988 I found 21-digit and 22-digit factors of F11 using Lenstra's recently-discovered elliptic curve method on a Fujitsu VP100. This completed the factorization

F11 = 319489 . 974849 . 167988556341760475137 . 3560841906445833920513 . p564,

The large factor p564 is a 564-digit prime number (proof by Morain).

The factorization was announced in [113, 115].

For details see my paper Factorization of the tenth Fermat number, Mathematics of Computation 68 (1999), 429-451.

Richard Brent