Quote:
Originally Posted by science_man_88
Iterations that hit 2,1,0,1,2 mod the mersenne, prior to the final iteration are either bad, or not prime. We also know (uselessly) that the residue has the same parity as the floor of the full number divided by the mersenne. Another useless fact is that a candidate factor can be tested using a modified LL test mod the candidate ( given at least 1 LL test using the mersenne). About the only interesting fact I come up with on the fly, is that a candidate mersenne prime, has to have an even multiple of the product of all previous mersenne primes( except maybe pairs of twin prime exponents), congruent to 2 mod the candidate.

Wow interesting. Does this last relationship hold for all the known mersenne primes?