This argument is called a heuristic. It's not actually a proof. It is an extremely persuasive one, however, and and as result of it, nearly all mathematicians

This argument is called a heuristic. It's not actually a proof. It is an extremely persuasive one, however, and and as result of it, nearly all mathematicians believe the conjecture is true. The persuasiveness of the heuristic is one of the things that makes the problem so confounding. It's obviously true; it's silly to argue that it isn't.