Definition:Meissel-Mertens Constant

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Definition

Consider the expression:

$\displaystyle M = \map {\lim_{n \mathop \to \infty} } {\sum_{\substack {p \mathop \le n \\ \text {$p$ prime} } } \dfrac 1 p - \ln \ln p}$

Then:

$M \approx 0 \cdotp 26149 \, 72128 \, 47642 \, 78375 \, 54268 \, 38608 \, 69585 \, 90516 \ldots$

This sequence is A077761 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


The constant $M$ is known as the Meissel-Mertens Constant.


Also known as

Also known as:


Also see


Source of Name

This entry was named for Daniel Friedrich Ernst Meissel and Franz Mertens.


Sources