Threw history,prime numbers has always be a great fascination for mathematicians. Even in modern times,primes numbers continues to fascinate many people.Probably the main reason why prime numbers continues to create such great interest would be because of the difficulty to prove that any given arbitrary number is prime. This is call the primality test. Most of the test for primality are probalistic rather than deterministic,because probalistic test are much more quicker than the deterministic ones. When testing the primality of a given number,one of the theorem that is very largely used is Fermat s little theorem: if "p" is a prime number that is not a factor of a given integer "a",then pow(a, p - 1) = 1 (mod p) or pow(a, p - 1) p = 1 One of the main application of prime numbers nowadays is chryptography,the RSA algorithm for encrypting and decrypting messages is based on prime numbers.- Threw history,prime numbers has always be a great fascination for mathematicians. Even in modern times,primes numbers continues to fascinate many people.Probably the main reason why prime numbers continues to create such great interest would be because of the difficulty to prove that any given arbitrary number is prime. This is call the primality test. Most of the test for primality are probalistic rather than deterministic,because probalistic test are much more quicker than the deterministic ones. When testing the primality of a given number,one of the theorem that is very largely used is Fermat s little theorem: if "p" is a prime number that is not a factor of a given integer "a",then pow(a, p- 1) = 1 (mod p) or pow(a, p- 1)　 p = 1 One of the main application of prime numbers nowadays is chryptography,the RSA algorithm for encrypting and decrypting messages is based on prime numbers.