Dr. Gosper, You math list might find the following announcement that I sent to Dr. Caldwell (of <A HREF="http://www.utm.edu/research/primes/">Prime Pages</A> fame) concerning a new lower factor bound for c5: http://www.isthe.com/chongo/tech/math/prime/index.html#c5 In particular: I am pleased to report a new lower factor bound for c5 = 2^(2^127-1)-1. I have confirmed my previous lower factor bound: http://www.utm.edu/research/primes/mersenne/index.html#c that I made when I was working at SGI. In addition, I have extended that result and have determined that c5 has no prime factor < 1e51. I used calc version 2.11 http://www.isthe.com/chongo/tech/comp/calc/index.html) running on AMD Athlon processors to verify and extend my previous result. Here is a quote that may be apt for index.html#c web page: Finding a factor of c5 will be a long shot. "Happiness is just around the corner" was one of the encouragements that Dr. Lehmer used to give to those who were deep in computational quests. Nevertheless the hope for finding c5 happiness is softened somewhat by the fact that c5 has an intractable number of corners. Landon Curt Noll http://www.isthe.com/chongo