DescriptionSum of reciprocals of primes.svg	English: A plot showing the sum of the reciprocal of the primes growing without bound. The x axis is ${\displaystyle n}$ and is logarithmic (labelled in evenly spaced powers of 10), going up to 106. A loose but still unbounded lower bound mentioned in the article (${\displaystyle \ln \ln(n+1)-\ln {\frac {\pi ^{2}}{6}}}$) is also shown for reference. Source used to generate this chart is shown below.
Date	21 March 2013
Source	Own work
Author	Dcoetzee
SVG development InfoField	The SVG code is valid.   This chart was created with Mathematica.    This chart uses embedded text that can be easily translated using a text editor.

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

primerecip = Table[][][n], {n, 1, 10^6}]; g[x_] := Apply[][][x]]; base = N[][10^6]/600)]; t = Table[][base^x]}, {x, 1, Floor[][base, 10^6] - 1}]; Show[][t, Joined -> True],   LogLinearPlot[][][x + 1] - Log[Pi^2/6], {x, 1, 10^6},    PlotStyle -> ColorData[1, 2], LabelStyle -> FontSize -> 14] 

LaTeX source for labels:

$$ \sum_{{\scriptstyle p\scriptsize\textrm{ prime }}\atop {\scriptstyle p\le n}}\frac1p $$ $$ \ln \ln (n+1) - \ln\frac{\pi^2}6 $$ 

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 in Inkscape.