More accurate estimates

The Riemann hypothesis is equivalent to the following statement.

$$\pi (x) -li (x) = O( \sqrt{x} \log x),$$

(von Koch, Acta Mathematica 24 (1901), 159-182).

L.Schoenfeld [56 #15581b] gave in 1976 a numerically explicit version of this equivalent form :

$$\vert\pi (x) -li (x)\vert \leq \frac{\sqrt{x}\log x}{8\pi}, \quad x \geq 2657.$$

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