1. How many contiguous zeros of zeta are known, to what height
2. How many contiguous primes are known, to what height
3. How many zeta zeros determine how many primes, to what exactness


For example, would knowing the first 1,000 zeta zeros pinpoint the location of the first 1,000 primes, exactly? (Assuming all zeros are on the critical line, which found ones appear to be)


Is there a formula that would match a certain number of zeta zeros to a certain number of primes that are determined. Or perhaps, could you calculate more than would be directly calculated by assuming RH, and find more primes. Would even the first 5 roots of zeta give any information on a large number of primes, etc.


I know these questions are very general, I sense that many zeta zeroes would need to be calculated to even find the first thousand primes roundable to their integer values, and even then some might round the wrong way?


PGH



Questions about the Riemann Zeta Function
You would need to know *all* the Riemann zeros to determine a single prime exactly, and vice versa. The primes and the zeros are on the opposite sides of a Fourier transform in Riemann's Explicit Formula, so the mathematical version of the Heisenberg Uncertainty Principle applies:


<http://en.wikipedia.org/wiki/Fourier_transform#Uncertainty_principle>


For the approximate values of small primes as determined by low-lying zeros, you might enjoy looking at <http://www.math.ucsb.edu/~stopple/explicit.html>


