Divergent Products over Prime Numbers

SUBSPECIES

$\displaystyle \prod_{\substack{p\in\mathbb{P} \\ p>2}} \, p = \dfrac{(2\pi)^2}{2} = 2\pi^2 \quad \textit{(stable)}$

$\displaystyle \prod_{\substack{p\in\mathbb{P} \\ p>2}} \, (p\!-\!1) = \dfrac{(2\pi)^2}{1\,\zeta(1)} = 4\pi^2 \quad \textit{(stable)}$

$\displaystyle \prod_{\substack{p\in\mathbb{P} \\ p>2}} \, (p\!+\!1) = \dfrac{24}{3} = 8 \quad \textit{(stable)}$

$\displaystyle \prod_{\substack{p\in\mathbb{P} \\ p>2}} \, \dfrac{p\!-\!1}{p\!+\!1} = \dfrac{4\pi^2}{8} = \dfrac{\pi^2}{2} \quad \textit{(stable)}$

$\displaystyle \prod_{\substack{p\in\mathbb{P} \\ p>2}} \, \dfrac{p\!+\!1}{p\!-\!1} = \dfrac{8}{4\pi^2} = \dfrac{2}{\pi^2} \quad \textit{(stable)}$

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