The Lucas-Lehmer test seems pretty magical to me and I have wanted to see a full proof of the theorem for some time. For a long time, there has been a proof online that M(p) divides the term in the LL sequence means that M(p) is prime but I had still never seen the other half. So I worked out the rest of a proof. If interested, please take a look at http://www.jt-actuary.com/lucas-le.htm. I see one "typo" where the "less than" symbol (<) displays incorrectly online. There may be other typos and even errors. (Well, I can hope not...) If this seems readable, would anyone want it linked in to a FAQ? (Not my call. I just wanted a proof.) Trivial note: back in the summer of 1968, I was one of a bunch of high school kids who met DH Lehmer (son of the Lehmer of LL fame, also a UC Berkeley math professor) in the basement of one of the engineering buildings at Berkeley. (It may have been a math building then, but the location is now an engineering building and the math buildings were in three other spots even then.) He showed us his "DLS-127" (Delay Line Sieve). This was one of the best prime-crunchers of the 1960's. As I recall, it was an ANALOG computer based on very precise inductors. Thanks, Joth _________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
