💁♂️: They are prime-lookalikes that passes Pierre de Fermat's "little theorem" inspired prime test
Little theorem - "if N is a prime number, then bN−b is always a multiple of N"
Prime test - the reverse of Little theorem be a test for prime, that by checking bN−b is a multiple of N for all values of b, then N must be prime
The composite numbers that breaks this prime test is known as Carmichael Numbers and the smallest of such numbers is 561
More concretely, the Carmichael Numbers are defined by Korselt's criterion
🤔: It was proven that there are also infinite amount of these numbers but mathematicians have no idea how they are distributed
A 17 year old teenager named Daniel Larsen showed a proof to determine if a gap will contain a Carmichael number that was not limited to very large numbers