Factorization of the tenth Fermat number

Abstract

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} .