Hmm, I wouldn't say that defining a prime number as a number n with prime factors 1 and a with 1 and a not necessarily distinct instantly breaks the FTA, but it

Hmm, I wouldn't say that defining a prime number as a number n with prime factors 1 and a with 1 and a not necessarily distinct instantly breaks the FTA, but it sure does make it a lot harder to state while still conveying the same idea otherwise.