THE FACTORIZATION OF THE 9TH FERMAT NUMBER

In this paper we exhibit the full prime factorization of the ninth Fer mat number F9 = 2(512) + 1. It is the product of three prime factors t hat 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 algor ithm that depends on arithmetic in an algebraic number field. In the p resent case, the number field used was Q(fifth-root 2) . The calculati ons were done on approximately 700 workstations scattered around the w orld, and in one of the final stages a supercomputer was used. The ent ire factorization took four months.