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.