> 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 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).
More recreational math from Cambridge students here: https://www.archim.org.uk/publications
But then, that long number wouldn't be a prime, so it's more like prime-ception. :)
In general, "fixing" a number such that it is divisible by a given prime is easy.