A Carmichael Number is a special type of composite number that satisfies Fermat's Little Theorem for all integers that are coprime to it. This means that if you take any integer a that does not share any factors with the Carmichael number n , then a^n-1 \equiv 1 \mod n . This property makes Carmichael numbers appear to be prime when they are actually not. The smallest Carmichael number is 561, which is the product of the primes 3, 11, and 17. Carmichael numbers are significant in number theory and cryptography because they can mislead primality tests, making them important for understanding the limitations of algorithms used to identify prime numbers.