# Definition:Meissel-Mertens Constant

## Definition

Consider the expression:

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

Then:

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

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

Also known as:

## Source of Name

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

## Sources

but beware -- there is a mistake in the formula they give