Summary

DescriptionMeissel–Mertens constant definition.svg	English: A plot showing the definition of the Meissel–Mertens constant as the difference in the limit between the sum of the reciprocals of primes p < n, and ln(ln(n)). The x axis is ${\displaystyle n}$ and is logarithmic (labelled in evenly spaced powers of 10), going up to 106. Source used to generate this chart is shown below.
Date	21 March 2013
Source	Own work   This W3C-unspecified diagram was created with Mathematica.
Author	User:Dcoetzee

Licensing

I, the copyright holder of this work, hereby publish it under the following license:

This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.

The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission. http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse

Source

All source released under CC0 waiver.

Mathematica source to generate graph (which was then saved as SVG from Mathematica):

primerecip = Table[N[1/Prime[n]], {n, 1, 10000000}];
g[x_] := Apply[Plus, Take[primerecip, PrimePi[x]]];
base = N[E^(Log[10^6]/600)];
t = Table[{base^x, g[base^x]}, {x, 1, Floor[Log[base, 10^6]] - 1}];
Show[ListLogLinearPlot[t, Joined -> True], 
 LogLinearPlot[Log[Log[x]], {x, 1, 10^6}, 
  PlotStyle -> ColorData[1, 2]], LabelStyle -> FontSize -> 14]

LaTeX source for labels:

$$ \sum_{{\scriptstyle p\scriptsize\textrm{ prime }}\atop {\scriptstyle p\le n}}\frac1p $$
$$ \ln(\ln(n)) $$

These were converted to SVG with [1] and then the graph was embedded into the resulting document in Inkscape. Axis fonts were also converted to Liberation Serif and arrow was added in Inkscape.