How can I prove that $\frac{x}{\ln(x)} < \pi(x)$ for $x \geq 17$?

Asked Feb 05 '23 at 06:11

Active Feb 05 '23 at 06:11

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I saw on Wikipedia that $\frac{x}{\ln(x)} < \pi(x)$ for $x \geq 17$ but it doesn't provide the proof. What is the proof for this and are there any legitimate papers that I can cite?

asked Feb 05 '23 at 06:11

rokkc

4

Wikipedia does not provide a proof but gives a reference. That paper by J. Barkley Rosser and Lowell Schoenfeld contains this inequality (Corollary 1) with a reference to D. N. Lehmer's list of primes. – Anne Bauval Feb 05 '23 at 07:03

How can I prove that $\frac{x}{\ln(x)} < \pi(x)$ for $x \geq 17$?

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