A remark on an inequality for the prime counting function

Details A remark on an inequality for the prime counting function A remark on an inequality for the prime counting function

2005-09-05

arxiv.org/abs/math/0509095v2

Mathematical Inequalities and Applications Vol. 10, No. 1 (2007), 9-13

Mathematics

Number Theory

Scientific paper

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.

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