I was curious about this:<p>> 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.<p>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?