If a term of the Lucas-Lehmer serie equals 0 modulo Mx, then if it is the last term Mx is prime else Mx is not prime (because next terms will be -2 ; 4 ; 4 ; 4...). In both cases, we needn't compute next terms. Checking if a term of the Lucas-Lehmer serie equals 0 can be done, for example, during the inverse transform or during the substraction. So, this test is cheap and it would not slow down the program. However, it would be interesting if and only if a term of the Lucas-Lehmer serie can be 0 before the last term. What do you think about this idea ?
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