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A remark on an inequality for the prime counting function

Research paper by Dietrich Burde

Indexed on: 23 Mar '07Published on: 23 Mar '07Published in: Mathematics - Number Theory



Abstract

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.