[cbright]

> But I don't know if it can be proven there do not exist non-prime P/Q values which produce an RSA keypair which can successfully encrypt/decrypt messages. I'm sure this isn't kosher for a real implementation, but I've never found an answer.

If p and q are coprime Carmichael numbers then RSA will still successfully encrypt and decrypt messages, though this will be less secure as p*q will have smaller prime factors and thus be easier to factor.