English

A remark on an inequality for the prime counting function

Number Theory 2007-05-23 v2

Abstract

We note that the inequalities 0.92xlog(x)<π(x)<1.11xlog(x)0.92 \frac{x}{\log(x)} <\pi(x)< 1.11 \frac{x}{\log(x)} do not hold for all x30x\ge 30, contrary to some references. These estimates on π(x)\pi(x) came up recently in papers on algebraic number theory.

Cite

@article{arxiv.math/0509095,
  title  = {A remark on an inequality for the prime counting function},
  author = {Dietrich Burde},
  journal= {arXiv preprint arXiv:math/0509095},
  year   = {2007}
}