In order to prove primality of a number, previously we required a list of primes. Eratosthenes, about 230 B.C., created his famous sieve, The Sieve of Eratosthenes. Nowadays we have methods to perform sieve and store a table of primes on a computer system. Fermat, 1640 , described one characteristic of primes in his famous theorem. The converse of this theorem is however not true. There are composite numbers which comply with this characteristic These numbers are called pseudoprimes. This application provides examples and programs about primes, pseudoprimes, Carmichael numbers, strong pseudoprimes and primality testing. Only definitions of the concepts are included.