I think the remark (which I ascribe, perhaps flippantly and wrongly to ultra-finitists) "How many more?" deserves some consideration. I hope its uncontroversial that humans will only ever have a finite stockpile of "discovered" primes in their arsenal. So the next question is can we figure out an estimate of where the boundary (on magnitude, which I think also gives an estimate of total number of) might be? Or even give a very loose upper bound with a convincing argument? Seems like it may be possible. I have no trick up my sleeve here, it was just a passing thought.