On the first sign change of $\theta (x)-x$

Abstract

Let $\theta (x)={\sum }_{p\le x}\log p$. We show that $\theta (x)<x$ for $2<x<1.39\cdot 10^{17}$. We also show that there is an $x<\exp (727.951332668)$ for which $\theta (x)>x.$

10 pages, 2 figures