File:Legendre's constant.svg
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Size of this PNG preview of this SVG file: 694 × 336 pixels. Other resolutions: 320 × 155 pixels | 640 × 310 pixels | 1,024 × 496 pixels | 1,280 × 620 pixels | 2,560 × 1,239 pixels.
Original file (SVG file, nominally 694 × 336 pixels, file size: 742 KB)
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English: The first 100,000 elements of the sequence (red line), where is the prime-counting function. Adrien-Marie Legendre conjectured in 1808 that this sequence would converge to a value of approximately 1.08366 (blue line), which became known as Legendre's constant. The actual limit was later shown to be exactly 1.
Français : En rouge, les 100 000 premiers termes de la suite , où est la fonction de compte des nombres premiers. Adrien-Marie Legendre a conjecturé en 1808 que cette suite converge vers un nombre valant approximativement 1,08366 (en bleu), qui est devenu la Constante de Legendre. Il a été prouvé plus tard que la limite exacte est 1. |
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Plotted in Maple and converted to SVG format in Inkscape by Ilmari Karonen, using the following Maple code by Sandrobt: with(numtheory): with(plots): a:=vector(100000-1,i->[i+1,evalf(log(i+1)-(i+1)/pi(i+1))]): b:=vector(100000-1,i->[i,1.08366]): display(plot(b, color = blue,thickness=3),plot(a, color = red), view=[1..100000,0.8..1.2]); |
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| Author | Sandrobt and Ilmari Karonen | ||||
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| SVG development |  This vector image was created with Inkscape, or with something else. |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:08, 15 June 2010 | | 694 × 336 (742 KB) | Ilmari Karonen (talk | contribs) | {{Information |Description={{en|1=The first 10,000 elements of the sequence <math>a_n = \ln(n) - \frac{n}{\pi(n)}</math> (red line), where <math>\pi</math> is the prime-counting function. [[:en:Adrien-Marie Legendre|Adrien |
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