On the first sign change of 𝜃(𝑥)-𝑥

Platt, D.; Trudgian, T.

doi:10.1090/mcom/3021

On the first sign change of $\theta (x) -x$
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by D. J. Platt and T. S. Trudgian PDF

Math. Comp. 85 (2016), 1539-1547 Request permission

Abstract:

Let $\theta (x) = \sum _{p\leq x} \log p$. 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 $\theta (x) >x.$

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