Ole Warnaar and Wadim Zudilin write:
The Riemann Hypothesis does not just “do better” than the Prime Number Theorem
— it is generally believed to be as good as it gets”. That is, we, or far-superior
extraterrestrial civilisations, will never be able to predict the distribution
of the primes any better than the Riemann Hypothesis does.
My question concerns the part: it is generally believed to be “as good as it gets”.
Assume the Riemann Hypothesis is proved. What, then, has to be proven to show that “it ain't can get better”. How can this be mathematically formulated?