@D.W 1 isn't a prime because it is a 'trivial' case. It isn't prime by definition. A number is a prime when it has exactly two different divisors.
@D.W. But {} and Σ* are, by definition, in P. So they should not be ignored. I feel like your answer should've been NO. And footnote: if you disregard {} and Σ* (but why would you ever do that), then yes.
Footnote [ ;) ]: I'm not attacking you personally it's just a trend I recently noticed that I don't quite understand.
@Auberon Yeah, that makes sense! I think the answer you describe is also a good one. (In other words, I'm not disagreeing with you.)
Here's one possible way to think about it. Suppose we think about theorems as "predictions" that will help us predict what the deal is with some future concrete problem we run into. Then a fact that is true for all but those two trivial cases is still pretty good at predicting the situation for future concrete problems, because most of the time the problems we have to deal with are not those trivial two cases.
