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PeterisP comments on The dangers of zero and one - Less Wrong
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Well, but you can (a) preform moderately extensive testing, and (b) do redundancy.
If you write 3 programs for verifying primeness (using different algorithms and possibly programming languages/approaches); and if all their results match, then you can assume a much higher confidence in correctness than for a single such program.
I think multiple programs wouldn't help very much unless they were run on different processors and written in different languages.
Yes. I agree. I am certainly not trying to say that 99.99% confidence in the primality status of a four digit number is not achievable.