All prime numbers formula_5 satisfy formula_6 for all integers formula_3 which are relatively prime to formula_5. This has been proven by the famous mathematician Pierre de Fermat. In most cases if a number formula_1 is composite, it does not satisfy this congruence equation. So, there exist not so many Carmichael numbers. We can say that Carmichael numbers are composite numbers that behave a little bit like they would be a prime number. 