I was looking at a paper of Dusart (his 1999 extention of Rosser's Theorem), where the author gives (without proof, but using the results proved in the rest of the paper) bounds for the prime counting function pi(n).(adsbygoogle = window.adsbygoogle || []).push({});

The minimum was [tex]\frac{x}{\log(x)}\left(1+\frac{0.992}{\log(x)}\right)[/tex] (for x >= 599) and the maximum was [tex]\frac{x}{\log(x)}\left(1+\frac{1.2762}{\log(x)}\right)[/tex] (for x >= 2).

Does anyone know of a stronger result for the upper bound, perhaps with a stronger restriction? In practice the lower bound sticks much closer to pi(n) than the upper bound. In any case Dusart gives a reference for his method of derivation, but I haven't tracked it down yet.

Edit: Since the new version of this site, I can't read it with Firefox -- the site crashes my browser.

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# Bounding pi(n)?

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