How far away(time wise), if this hasn't already been happening, is prime coin from discovering previously unfound primes?
It's basically happening all the time (similarly with every software that's generating large primes, such as many encryption programs). Primes are not really sparse, so when you find a (large) prime, the probability that no one found it before you it is pretty high, and finding previously unfound primes is neither interesting nor hard. There are special kinds of primes (for example Mersenne primes) whose properties make it possible to prove their primality for much bigger values than is possible for randomly picked numbers, so the absolutely biggest prime numbers are typically of these kinds, but primecoin does not search for such primes.
What primecoin does is searching for special patterns (cunningham chains) of primes which are much rarer, so the task is usable as a proof-of-work mechanism. It is not yet clear whether the results will have practical uses outside of their primary use of protecting the primecoin blockchain, but it is conceivable that when research around some theorem around primes and cunningham chains needs many relatively long chains, the data will be welcome by researchers.
Onkel Paul
