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wedrifid comments on What Cost for Irrationality? - Less Wrong
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I think that the above only gives the odds that there are no such primes unless there is some good deep reason (presumably a set of symmetries, which doesn't seem at all likely since billion is an arbitrary seeming round decimal) for there to be some such prime or primes. Without that caveat, such statements would bite-in-the-ass far too many people historically who would have made overly confident mathematical claims. To clarify; I think you should be ridiculously confident, but not as confident as your reasoning by itself would justify.
I agree (and voted accordingly). The influence of the direct probability I calculated would be utterly overwhelmed in my confidence calculation compared to meta-uncertainty. I certainly wouldn't go as far as placing 1:10,000 odds, for example, even though my calculations would put it at 1^(-lots). In fact, I can't even assign extreme odds to something as obvious as there is no Jehova, except for signalling purposes. I know enough about the way me (and my species) think that assigning extreme probabilities would be ridiculously overconfident. (How this relates to things like Pascal's wager is a different and somewhat more philosophically difficult problem.)
This would be 1.
Something does seem to be missing in that expression.