We describe the complete factorization of the tenth Fermat number
F
10
F_{10}
by the elliptic curve method (ECM).
F
10
F_{10}
is a product of four prime factors with 8, 10, 40 and 252 decimal digits. The 40-digit factor was found after about 140 Mflop-years of computation. We also discuss the complete factorization of other Fermat numbers by ECM, and summarize the factorizations of
F
5
,
…
,
F
11
F_5, \dots , F_{11}
.