File:PrimeNumberTheorem.svg

From formulasearchengine
Jump to navigation Jump to search

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

This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.

Summary

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

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:
  • to share – to copy, distribute and transmit the work
  • 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.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

18 June 2011

image/svg+xml

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current18:49, 18 April 2022Thumbnail for version as of 18:49, 18 April 2022500 × 306 (26 KB)wikimediacommons>Nomen4Omenschmalere Kurven

There are no pages that use this file.