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bentarm comments on The dangers of zero and one - Less Wrong
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I was about 80% sure that 1159 was not prime, based on reading that sentence. It took me <1 minute to confirm this. I can totally be more than 99.99% sure of the primality of any given four-digit number.
In fact, those odds suggest that I'd expect to make one mistake with probability >0.5 if I were to go through a list of all the numbers below 10,000 and classify them as prime or not prime. I think this is ridiculous. I'm quite willing to take a bet at 100 to 1 odds that I can produce an exhaustive list of all the prime numbers below 1,000,000 (which contains no composite numbers), if anyone's willing to stump up at least $10 for the other side of the bet.
You can only simply exponentiate the chance of success if it doesn't correlate over multiple repetitions. I would say that if the list of primes below 10^6 you were referencing has at least one error in the first 10^5, it would be more likely to be faulty later, and vice versa, which means that your gut estimates on the two scales might be noncontradictory.
Right. Say you write code to generate primes. If there's no bug, all your answers are correct. If there's a bug in your code, probably lots of your answers are incorrect.