Meissel-Mertens constant

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The Meissel-Mertens constant (also known as Mertens' constant, Kronecker's constant, the Hadamard-de la Vallée-Poussin constant, or prime reciprocal constant) is $$M=\displaystyle\lim_{n \rightarrow \infty} \left( \displaystyle\sum_{p \leq n;p \mathrm{\hspace{2pt} prime}} \dfrac{1}{p} - \log(\log(n)) \right).$$ Note that the sum $\displaystyle\sum_{p \leq n;p \mathrm{\hspace{2pt} prime}} \dfrac{1}{p}$ diverges, so this definition resembles that of the Euler-Mascheroni constant.


Meissel-Mertens constant in terms of the Euler-Mascheroni constant

See Also

Euler-Mascheroni constant