Recall the Lucas Lehmer primality test for Mersenne primes which claims the following:
is prime iff
where and .
Does anyone know the details to the proof of this important theorem? I've been trying to work it out on my own, but its tough.
I'm finding that for prime Mersennes , one doesn't necessarily need to have in order for .
Consider the prime for instance. If is in the following set we have that .
{3,4,10,18,21,27,37,38,43,44,46,49,51,52,54,63,64, 73,75,76,78,81,83,84,89,90,100,106,109,117,123,124 }
I'm guessing there is a probalistic reason for this occurence. Anyone wanna try to work through it with me?