It is known that $|\pi(x) - \mathrm{li}(x)| < O(\sqrt{x}\log{x})$ follows from Riemann Hypothesis. But are there any better known approximations that would make the bounding function grow at a smaller rate?
great danger of a reopening - we still need a downvote and delete-votes to prevent that. Of course the question coudl still be undeleted after this , but at least we should try to delete it.
