On the first sign change of $θ(x) - x$

Abstract

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

10 pages, 2 figures