English

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

Number Theory 2014-07-09 v1

Abstract

Let θ(x)=pxlogp\theta(x) = \sum_{p\leq x} \log p. We show that θ(x)<x\theta(x)<x for 2<x<1.3910172<x< 1.39\cdot 10^{17}. We also show that there is an x<exp(727.951332668)x<\exp(727.951332668) for which θ(x)>x.\theta(x) >x.

Keywords

Cite

@article{arxiv.1407.1914,
  title  = {On the first sign change of $\theta(x) - x$},
  author = {Dave Platt and Tim Trudgian},
  journal= {arXiv preprint arXiv:1407.1914},
  year   = {2014}
}

Comments

10 pages, 2 figures