Apparently, from time to time, someone will come up with a newly discovered, very large

prime number.

However, it has been my understanding (or misunderstanding) that, if true, RH would

transform the PNT from a good estimate to an exact formula for generating the primes up to

n or for coming up with the nth prime.

I'm guessing that this must not be the case, since if it were, one could simply assume the

truth of RH (as, apparently, many mathematicians do in their mathematical papers), amend

the PNT in line with this, and proceed to generate n primes (or any particular nth prime).

Is something like this being done to generate all those zeros on the critical line?

Is there any simple(?) way of describing the relationship between the zeroes and the primes?

Thanks.