Image:PrimeNumberTheorem.png

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Displayed is

  • the number of primes less than or equal to x, labelled Π(x) (blue)
  • an approximation using \frac{x}{\ln{x}} (green)
  • an approximation using the logarithmic integral \operatorname{Li}(x) (red)

Created with Maple: plot({[seq([x,pi(x)],x=0..100000)],x/ln(x),Li(x)-Li(2)},x=0..100000,Pi[x]=0..10000,color=[blue,green,red]);

Author: FredStober


Public domain This image has been released into the public domain by its author, FredStober. This applies worldwide.

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FredStober grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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File history

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Date/TimeDimensionsUserComment
current20:16, 4 January 2006738×563 (15 KB)Fred Stober
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