A still sharper region where π(x) - li(x) is positive

Abstract

We consider the least number x for which a change of sign of π(x) - li(x) occurs. First, we consider modifications of Lehman's method that enable us to obtain better estimates of some error terms. Second, we establish a new lower bound for the first x for which the difference is positive. Third, we use numerical computations to improve the final result.