Wow, number theory was once my thing... Carmichael numbers are interesting indeed. Their very existence indicates that the "true nature" of primes is more obsc

Wow, number theory was once my thing... Carmichael numbers are interesting indeed. Their very existence indicates that the "true nature" of primes is more obscure and complicated than people of the earlier ages thought. Some applies to regular and irregular primes. If all primes were regular, Fermat's Last Theorem would have been a lot easier to prove. It is possible that Fermat himself was mistaken and saw the outlines of the proof for regular primes. Also, maths is one of the last remaining sciences where a fresh insight from a relative newbie can still move major, century-old obstacles.