Primality deterministic and primality probabilistic tests

In this paper the A. comments the importance of prime numbers in mathematics and in cryptography. He remembers the very important researches of Eulero, Fermat, Legen-re, Rieman and others scholarships. There are many expressions that give prime numbers. Between them Mersenne’s primes have interesting properties. There are also many conjectures that still have to be demonstrated or rejected. The primality deterministic tests are the algorithms that permit to establish if a number is prime or not. There are not applicable in many practical situations, for instance in public key cryptography, because the computer time would be very long. The primality probabilistic tests consent to verify the null hypothesis: the number is prime. In the paper there are comments about the most important statistical tests