7058*10^23216 - 1 may be prime. (a = 2) 7058*10^23216 - 1 is prime! (P = 5, Q = -1) [23220 digits] The primality of this number, of the form k*b^n - 1, was proved by computing a Lucas sequence. The result is verified by computing another independent Lucas sequence. See http://en.wikipedia.org/wiki/Lucas_sequence