# Prime Product

It is a well known result that

$\prod _{p \text{ is prime}}\dfrac{1-p^{-2}}{1+p^{-2}}=\dfrac{2}{5}$

Now, if

$\displaystyle \large \prod _{ p\equiv-1\pmod4 }\dfrac{1-p^{-2}}{1+p^{-2}}=\frac{AG}{\pi^B},$

where $$A$$ and $$B$$ are integers with $$G$$ denotes the Catalan's constant. Find $$A+B$$.

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