this is for holding javascript data
Benedict Irwin edited untitled.tex
almost 8 years ago
Commit id: 1e41150fbbdf8da28e05481749779c163f0cf3b4
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\end{equation}
Then if we set $x=1$, and change the infinite sums to $n$ (checked that the series are generated at the same rate) we should have have the prime counting function
\begin{equation}
\sum_{q\in\mathbb{P}}^n 1 = \log\left(\frac{\prod_{k=1}^n 2}{\exp\left(\sum_{q\notin\mathbb{P}}^n \frac{1}{q}\sum_{p|q}
(-1)^{q+1}p^*(q)\right)}\right)\\
\pi(n) = \log\left(\frac{\prod_{k=1}^n 2}{\exp\left(\sum_{q\notin\mathbb{P}}^n \frac{1}{q}\sum_{p|q} (-1)^{q+1}p^*(q)\right)}\right)
\end{equation}