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Chebyshev-Sylvester Constant

In 1891, Chebyshev and Sylvester showed that for sufficiently large $x$, there exists at least one prime number $p$ satisfying


where $\alpha=0.092\ldots$. Since the Prime Number Theorem shows the above inequality is true for all $\alpha>0$ for sufficiently large $x$, this constant is only of historical interest.


Le Lionnais, F. Les nombres remarquables. Paris: Hermann, p. 22, 1983.

© 1996-9 Eric W. Weisstein