A Carmichael number is a special type of composite number that passes certain tests for primality, making it appear to be prime. Specifically, these numbers satisfy Fermat's Little Theorem for all integers that are coprime to them, which means they can fool some primality tests. The smallest Carmichael number is 561, and they are also known as "absolute pseudoprimes." Unlike prime numbers, Carmichael numbers have divisors other than 1 and themselves, yet they can mislead algorithms designed to identify primes, highlighting the complexities in number theory and the importance of reliable primality testing methods.