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Gurkenglas comments on The dangers of zero and one - Less Wrong
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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.