MAKE A MEME View Large Image Sum of reciprocals of primes.svg en A plot showing the sum of the reciprocal of the primes growing without bound The x axis is <math>n</math> and is logarithmic labelled in evenly spaced powers of 10 going up to 10<sup>6</sup> A loose but ...
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Keywords: Sum of reciprocals of primes.svg en A plot showing the sum of the reciprocal of the primes growing without bound The x axis is <math>n</math> and is logarithmic labelled in evenly spaced powers of 10 going up to 10<sup>6</sup> A loose but still unbounded lower bound mentioned in the article <math>\ln \ln n+1 - \ln\frac \pi 2 6</math> is also shown for reference Source used to generate this chart is shown below own User Dcoetzee 2013-03-21 Prime numbers Cc-zero Source All source released under CC0 waiver Mathematica source to generate graph which was then saved as SVG from Mathematica <pre> primerecip Tablen n 1 10 6 ; gx_ Applyx; base N10 6/600 ; t Tablebase x x 1 Floorbase 10 6 - 1 ; Showt Joined -> True LogLinearPlotx + 1 - LogPi 2/6 x 1 10 6 PlotStyle -> ColorData1 2 LabelStyle -> FontSize -> 14 </pre> LaTeX source for labels <pre> \sum_ \scriptstyle p\scriptsize\textrm prime \atop \scriptstyle p\le n \frac1p \ln \ln n+1 - \ln\frac \pi 2 6 </pre> These were converted to SVG with http //www tlhiv org/ltxpreview/ and then the graph was embedded into the resulting document in Inkscape Axis fonts were also converted to Liberation Serif in Inkscape
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