> Finally, I generated random fluctuations in the number and tested each with the Miller-Rabin primality test. This produced a shortlist of numbers which were very very likely to be prime. I used Dario Alpern’s fantastic tool to determine whether any of them actually were prime.
I thought that in crypto one normally just repeats Miller-Rabin enough times that it's infinitesimally improbable that the candidate isn't a prime, and that the reason for doing this is that it's too expensive to actually prove it. This indicates that it's now feasible to just prove that a number is actually prime; should crypto libraries now switch to a different method of ensuring primality?
From an engineering point of view it really does not matter. The chance that the probabilistic algorithm fails is so insignificantly small, that cosmic rays hitting your CPU registers is probably a bigger problem.
From a mathematical/CS point of view, indeed it was a fairly recent, and fairly pleasant discovery that the primality testing algorithm can be derandomized while still retaining its low complexity (it was suspected for a long time, but proving it was awesome).
> Finally, I generated random fluctuations in the number and tested each with the Miller-Rabin primality test. This produced a shortlist of numbers which were very very likely to be prime. I used Dario Alpern’s fantastic tool to determine whether any of them actually were prime.
I thought that in crypto one normally just repeats Miller-Rabin enough times that it's infinitesimally improbable that the candidate isn't a prime, and that the reason for doing this is that it's too expensive to actually prove it. This indicates that it's now feasible to just prove that a number is actually prime; should crypto libraries now switch to a different method of ensuring primality?