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File:PrimeNumberTheorem.svg

Original file ‎(SVG file, nominally 500 × 306 pixels, file size: 26 KB)

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Summary

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Description
English: Displayed is
  • the number of primes less than or equal to the abscissa (red)
  • an approximation using (green)
  • an approximation using the logarithmic integral (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  ;
  • en vert, une approximation utilisant  ;
  • en bleu, une approximation utilisant l'intégrale logarithmique .)
Date
Source Own work
Author Noel Bush

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
You are free:
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  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

File history

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Date/TimeThumbnailDimensionsUserComment
current16:49, 18 April 2022Thumbnail for version as of 16:49, 18 April 2022500 × 306 (26 KB)Nomen4Omen (talk | contribs)schmalere Kurven
18:37, 19 October 2011Thumbnail for version as of 18:37, 19 October 2011500 × 306 (22 KB)Bender2k14 (talk | contribs)added nominal dimensions to workaround this [https://bugzilla.wikimedia.org/show_bug.cgi?id=19543 bug]
20:59, 18 June 2011Thumbnail for version as of 20:59, 18 June 2011512 × 512 (23 KB)Noel Bush (talk | contribs)fixed image padding so axis labels are fully visible
10:49, 18 June 2011Thumbnail for version as of 10:49, 18 June 2011512 × 512 (22 KB)Noel Bush (talk | contribs)

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