A remark on an inequality for the prime counting function

Dietrich Burde

Published 2005-09-05, updated 2007-03-23Version 2

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