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Mertens Theorem

\lim_{x\to\infty} {\prod\nolimits_{\scriptstyle 2\leq p\leq ...
\left({1-{1\over p}}\right)\over {e^{-\gamma}\over\ln x}}=1,

where $\gamma$ is the Euler-Mascheroni Constant and $e^{-\gamma}=0.56145\ldots$.


Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, p. 351, 1979.

Riesel, H. Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 66-67, 1994.

© 1996-9 Eric W. Weisstein