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 . p_{564},

The large factor p_{564} 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.