mpz_probab_prime_p reproducibility

[Pierre Chatelier]

Hello,

I would like to know if two runs of mpz_probab_prime_p(N, 50) for the same number N, on two different machines, trigger the same probabilistic primality tests.

If this is the case, is there at the current time, a known M value, such that for each integer N < M, the probabilistic answer of mpz_probab_prime_p(N, 50) is exact ?
In other words, is there any known integer N for which mpz_probab_prime_p(N, 50) is wrong or unsure ?

Regards,

Pierre Chatelier