Function isPrime(number):
    return false

Accurate for almost 100% of cases

Any algorithm can be O(1) if you cache all the answers beforehand.

Yes.

And depending how occasionally we’re talking, I can code for some very fast solutions when the correctness requirements are low enough.

Alternately, if we want it to only be occasionally fast, I’ve got a very nice looking and very wrong algorithm for that, as well.