# Prime Product

**Number Theory**Level 5

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 \(A+B\).