A remark on an inequality for the prime counting function

Dietrich Burde

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A remark on an inequality for the prime counting function

Dietrich Burde

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Abstract

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

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Dietrich Burde. 2007-03-23. A remark on an inequality for the prime counting function. https://arxiv.org/abs/math/0509095

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