GIMPS double-checking certainty rate

[GP2]

Originally Posted by 6pac

An idea (if I understand correctly though) would be to get a candidate with floating-point math and just for the fun, try to get "100% certainty" on it using a second pass.

If your primary concern is the roundoff error (convolution error) associated with floating-point math, then you could try using a ridiculously large FFT size.

It would take considerably longer, but presumably not as long as 10 years, or whatever your hypothetical fixed-point calculation would require.

Perhaps there are some theoretical bounds that could be determined for a given exponent using a particular FFT size, such that we could guarantee that the error will always be less than 0.5?

Another approach is to use the relatively new Gerbicz PRP tests rather than the LL test. It has a much greater level of built-in error correction, which would make us considerably more confident of the final result even when there is only a single test.

[retina]

Originally Posted by GP2

If your primary concern is the roundoff error (convolution error) associated with floating-point math, then you could try using a ridiculously large FFT size.

It would take considerably longer, but presumably not as long as 10 years, or whatever your hypothetical fixed-point calculation would require.

Perhaps there are some theoretical bounds that could be determined for a given exponent using a particular FFT size, such that we could guarantee that the error will always be less than 0.5?

Another approach is to use the relatively new Gerbicz PRP tests rather than the LL test. It has a much greater level of built-in error correction, which would make us considerably more confident of the final result even when there is only a single test.

I think we are good enough as far as certainty goes. I personally have no problem accepting 1 in 2^64 as enough proof. If that kind of proof level is worrying to anyone then they have much more pressing concerns with being struck by lightning.