Carmichael number

A Carmichael number is a composite number that satisfies a specific mathematical condition, making it appear prime under certain tests. This condition is related to Fermat's Little Theorem, which states that for any prime number p and any integer a not divisible by p, a^p - a is divisible by p.

While a prime number will always satisfy this, the converse is not always true for composite numbers. A composite number n that satisfies this condition for a base a (where a and n are relatively prime) is called a Fermat pseudoprime. Carmichael numbers are special Fermat pseudoprimes because they satisfy this condition for all bases a that are relatively prime to n. The smallest Carmichael number is 561.12