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Calculus Level 5

Let \( p \) be the set of prime numbers. If

\[\prod _{ p }^{ }{ \left( \sum _{ n=0 }^{ \infty }{ { p }^{ -4n } } \right) } =\frac { { \pi }^{ A } }{ B } , \] where \(A, B \) are positive integers, find \( A + B \).

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