Quote:
Originally Posted by dominicanpapi82
If you start the test right from the beginning, from S(1) = 4 or 10 or one of the other valid STARTING values of the sequence, i.e. S(1) but not S(2) or S(3), etc, assuming a perfect computer with infinite and infallible accuracy (or, say, an omnipotent God) can the test ever go into a loop or zero out before the end of the test? Is this even known?

I've studied the LucasLehmer sequence quite a bit over the past year, and based on all of the empirical evidence that I've collected, I have concluded that the LL sequence will zero out after any number of terms only for prime modulii, and furthermore, initiating the sequence with a "natural start" of 4, will zero out only on the P1 term. Of course, I would welcome a contradiction so I can finally put this Lemma to bed.