All odd numbers are prime: 1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime, and so on, I don't have funding to check all of them, but it suggests an avenue of productive further work.
Look, just because it breaks everything, that's no reason not to include it in a joke. We'll just have to rebuild the entire edifice of mathematics.
Seriously, thanks for the link, I hadn't considered the implications of including 1 in the set of primes, and it really does seem to break a lot of ideas.