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

We consider the least number x x for which a change of sign of π (x) − l i (x) (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 smaller upper bound for the first x x for which the difference is positive. Third, we use numerical computations to improve the final result.