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.