5.4 $\pi_b'[x]$: First-Order Derivative of Base Prime Counting Function

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The Fourier series for the first-order derivative $\pi_b'[x]$ of the base prime counting function evaluates to $2\ f$ at prime integers where $f$ is the evaluation frequency limit.


First-Order Derivative of Fundamental Prime Counting Function (i.e. p'[x]) Evaluated at f=1.
$\pi_b'[x]$ evaluated at $f=1$.

First-Order Derivative of Fundamental Prime Counting Function (i.e. p'[x]) Evaluated at f=1.
$\pi_b'[x]$ evaluated at $f=1$.
First-Order Derivative of Fundamental Prime Counting Function (i.e. p'[x]) Evaluated at f=2.
$\pi_b'[x]$ evaluated at $f=2$.
First-Order Derivative of Fundamental Prime Counting Function (i.e. p'[x]) Evaluated at f=3.
$\pi_b'[x]$ Evaluated at $f=3$.


First-Order Derivative of Fundamental Prime Counting Function (i.e. p'[x]) around x=19 Evaluated at f={2, 4, 8}.
$\pi_b'[x]$ around $x=19$ evaluated at $f={2, 4, 8}$.