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Summary

DescriptionPrimeNumberTheorem.svg	English: Displayed is the number of primes less than or equal to the abscissa $x$ (red) an approximation using ${\frac {x}{\ln {x}}}$ (green) an approximation using the logarithmic integral $\operatorname {Li} (x)$ (blue) Created using Mathematica: Plot[{PrimePi[x], x/Log[x], LogIntegral[x] - LogIntegral[2]}, {x, 0, 100000}, PlotStyle -> {Red, Green, Blue}] (An SVG recreation of File:PrimeNumberTheorem.png from Wikimedia Commons.) Français : Une illustration du théorème des nombres premiers : en rouge, le nombre de nombres premiers inférieurs ou égaux à $x$ ; en vert, une approximation utilisant ${\frac {x}{\ln {x}}}$ ; en bleu, une approximation utilisant l'intégrale logarithmique $\operatorname {Li} (x)$ .)
Date	18 June 2011
Source	Own work
Author	Noel Bush

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