From crandall@reed.edu Tue Jan 7 01:07:27 1997
Date: Mon, 6 Jan 1997 17:42:03 -0500
From: Richard E Crandall
To: NMBRTHRY@LISTSERV.NODAK.EDU
Subject: New factor of the 16th Fermat Number
On 4 Jan 1997, Richard Crandall and Karl Dilcher found a 27-digit
prime factor of F_16 = 2^(2^16)+1. It is now known that
F_16 = 825753601 * 188981757975021318420037633 * composite
The first factor was found by Selfridge in 1953, and the composite
character of the cofactor has been proven by Richard Brent, who has
also found the precise curve orders relevant to the new factor.
The method used was ECM/DWT (Elliptic curve method with discrete
weighted transform), with a large-GCD implementation by Joseph Buhler.
The DWT is used for the large-integer multiplication. Enhancements of
ECM due to Peter Montgomery, Harvey Dubner, and Brent were also
employed.