Carmichael numbers

Carmichael numbers are special composite numbers that pass certain tests for primality, which makes them appear to be prime when they are not. Specifically, they satisfy Fermat's Little Theorem for all integers coprime to them, meaning they behave like prime numbers in certain mathematical checks. This can be misleading in number theory, as most composite numbers fail these tests. The smallest Carmichael number is 561. They are significant in cryptography and number theory because they challenge our understanding of how to identify prime numbers reliably.