The factorization of the ninth Fermat number
Abstract
In this paper we exhibit the full prime factorization of the ninth Fermat number {F_9} = {2^{512}} + 1 . It is the product of three prime factors that have 7, 49, and 99 decimal digits. We found the two largest prime factors by means of the number field sieve, which is a factoring algorithm that depends on arithmetic in an algebraic number field. In the present case, the number field used was {Q}(√[5]{2}) . The calculations were done on approximately 700 workstations scattered around the world, and in one of the final stages a supercomputer was used. The entire factorization took four months.
 Publication:

Mathematics of Computation
 Pub Date:
 July 1993
 DOI:
 10.1090/S00255718199311829534
 Bibcode:
 1993MaCom..61..319L
 Keywords:

 Fermat number;
 factoring algorithm