The classical Lucas-Lehmer test gives necessary and sufficient conditions for the primality of 2 p -1, p an odd prime. Such primes are called Mersenne primes. Here, taking b = 2 and a = 3 to be integers, and p to be an odd prime, we give probable prime tests for (b p+1)/(b +1) and (a p -1)/(a -1) that are analogous to the classical Lucas-Lehmer test
