Let me quote about the LL test from
www.mersenne.org/math.htm
Quote:
The LucasLehmer primality test is remarkably simple. It states that for P > 2, 2P1 is prime if and only if Sp2 is zero in this sequence: S0 = 4, SN = (SN12  2) mod (2P1). For example, to prove 27  1 is prime:
Code:
S0 = 4
S1 = (4 * 4  2) mod 127 = 14
S2 = (14 * 14  2) mod 127 = 67
S3 = (67 * 67  2) mod 127 = 42
S4 = (42 * 42  2) mod 127 = 111
S5 = (111 * 111  2) mod 127 = 0

Now how could we start at S5? We don't know the answer. In fact, if we did, we wouldn't have to run the test because the
only thing we're interested in is the answer to the very last step in the (long) sequence. If it turns out to be 0, the number is prime. Any other value and the number is composite.