5.3.2, due November 22

First question: does the Lucas-Lehmer test always work for Mersenne primes? (It sounds like it does.) This proof is a great idea but it is far from intuitive and the proof was extremely difficult for me to follow. I know we already talked about this, but that is a huge number that we know is prime! It's cool that mathematics has so much left undiscovered. I think that's one reason I love it so much.