Prime Product

It is a well known result that

p is prime1p21+p2=25\prod _{p \text{ is prime}}\dfrac{1-p^{-2}}{1+p^{-2}}=\dfrac{2}{5}

Now, if

p1(mod4)1p21+p2=AGπB,\displaystyle \large \prod _{ p\equiv-1\pmod4 }\dfrac{1-p^{-2}}{1+p^{-2}}=\frac{AG}{\pi^B},

where AA and BB are integers with GG denotes the Catalan's constant. Find A+BA+B.

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