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

Saouter, Yannick; Trudgian, Tim; Demichel, Patrick

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

Date

2013

Authors

Saouter, Yannick

Trudgian, Tim

Demichel, Patrick

Publisher

American Mathematical Society

Abstract

We consider the least number x for which a change of sign of Ï€(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.