English: The first 10, 000 000 elements of the sequence a_n = \ln(n) - \frac{n}{\pi(n)} (red line), where π 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.
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Plotted in Maple and converted to SVG format in Inkscape by Sandrobt, using the following Maple code:
> with(numtheory);
> with(plots);
> b := vector(10000, proc (i) options operator, arrow; [1000*i, 1.08366] end proc);
> c := vector(10000, proc (i) options operator, arrow; [1000*i, 1] end proc);
> a := vector(10000, proc (i) options operator, arrow; [1000*i, evalf(log(1000*i)-1000*i/pi(1000*i))] end proc);
> display(plot(b, color = blue, thickness = 3), plot(a, color = red), plot(c, color = black, thickness = 3), view = [1 .. 10000000, .95 .. 1.1]);
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{{Information |Description={{en|1=The first 10, 000 000 elements of the sequence a_n = \ln(n) - \frac{n}{\pi(n)} (red line), where π is the prime-counting function. Adrien-Marie Legendre conjectured in 1808 that this sequence would converge to a value of
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