Is 149 a prime? Take as long as you need to convince yourself (by math or by Google) that it is. Is it unreasonable to have 99.9...% confidence with quite a few nines (and an occasional 7) in there? Now let's say that you have a tax accountant, Bob, a decent guy that seems to be doing a decent job filing your taxes. You start chatting with Bob and he reveals that he's pretty sure that 149 isn't a prime. He doesn't know two numbers whose product is 149, it just feels unprimely to him. You try to reason with him, but he just chides you for being so arrogant in your confidence: can't you just agree to disagree on this one? It's not like either of you is a numbers theorist. His job is to not get you audited by the IRS, which he does, not factorize numbers. Are you a little bit worried about trusting Bob with your taxes? What if he actually claimed to be a mathematician?

You know, about that.