File:Meissel–Mertens constant definition.svg

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

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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.