Summary edit

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.

Licensing edit

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 edit

All source released under CC0 waiver.

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.