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Summary

DescriptionPlotDelta.gif	English: This plot illustrates normalized fluctuations of the prime-counting function $\pi (x)$ on the logarithmic scale. The red line represents Δ-function, while the blue curve represents similar function where $\pi _{0}(x)$ is replaced by $\mathrm {li} (x)$ , so one can compare the fluctuations with the difference between $\pi (x)$ and $\mathrm {li} (x)$ . The image was built by Droog_Andrey using Wolfram Mathematica 7.0 as follows: `LogLinearPlot[{(PrimePi[x] - RiemannR[x] + 1/Log[x] - ArcTan[Pi/Log[x]]/Pi)Log[x]/Sqrt[x], (LogIntegral[x] - RiemannR[x] + 1/Log[x] - ArcTan[Pi/Log[x]]/Pi)Log[x]/Sqrt[x]}, {x, 1, Exp[14]}, PlotPoints -> 10000, PlotRange -> All, PlotStyle -> {Red, Blue}, AxesOrigin -> {1, 0}, AspectRatio -> 1/2, AxesStyle -> Thick, TicksStyle -> Directive[Thick, Bold, 16]]`
Date	4 May 2007 (original upload date)
Source	Transferred from en.wikipedia to Commons.
Author	Droog Andrey at English Wikipedia

Licensing

This work has been released into the public domain by its author, Droog Andrey at English Wikipedia. This applies worldwide.
In some countries this may not be legally possible; if so:
Droog Andrey grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Original upload log

The original description page was here. All following user names refer to en.wikipedia.

Date/Time	Dimensions	User	Comment
2011-01-01 15:39	800×400× (39780 bytes)	Droog Andrey
2011-01-01 15:30	1440×720× (91313 bytes)	Droog Andrey
2008-08-29 17:03	800×480× (47370 bytes)	Droog Andrey	==Summary== This plot illustrates normalized fluctuations of the [[prime-counting function]] <math>\pi(x)</math> on the logarithmic scale. The red curve represents [[Prime-counting function#Formulas_for_prime-counting_functions\|delta function]], while th
2007-05-04 06:59	800×480× (18505 bytes)	Droog Andrey	This plot illustrates normalized fluctuations of the [[prime counting function]] <math>\pi(x)</math> on the logarithmic scale. The red curve represents [http://en.wikipedia.org/wiki/Prime_counting_function#Formulas_for_prime_counting_functions Delta func

File history

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	Date/Time	Dimensions	User	Comment
current	02:13, 16 May 2016	800 × 400 (39 KB)	OgreBot	(BOT): Reverting to most recent version before archival
	02:13, 16 May 2016	1,440 × 720 (89 KB)	OgreBot	(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2011-01-01 15:30:28 by Droog Andrey
	02:13, 16 May 2016	800 × 480 (46 KB)	OgreBot	(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2008-08-29 17:03:13 by Droog Andrey
	02:13, 16 May 2016	800 × 480 (18 KB)	OgreBot	(BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2007-05-04 06:59:52 by Droog Andrey
	01:01, 11 May 2016	800 × 400 (39 KB)	NMaia	Transferred from en.wikipedia