The reason we don't like 1 being prime is because it makes stating lots of theorems that involve primes (in particular, the fundamental theorem of arithmetic) r

The reason we don't like 1 being prime is because it makes stating lots of theorems that involve primes (in particular, the fundamental theorem of arithmetic) really tedious. No, it makes the FTA wrong! If one were prime, then every number would have infinitely many prime factorizations instead of one unique one. you'd have to say "For every non-unitary prime," etc. In the even/odd case, one could just as easily say "for every non-zero odd number." This isn't somehow an argument that applies only to the question of one's primality. Zero being even is a consequence of the above definition of even ...as is one not being prime a consequence of the definition of primes. A prime is a number with exactly two distinct factors. One only has one distinct factor, therefore it is not prime. If you don't buy this definition, or if you claim that I'm gerrymandering the definition to suit my preference that one not be prime, be aware that a reasonable person could make the same claim about the definition of even numbers, viz., that it was chosen for convenience. While it's might be entertaining to argue about such chicken-and-egg problems, at the end of the day the evidence is pretty clearly in favor of the properties proceeding from the definition in both cases.