# Inspired by Me

Calculus Level 3

Let

$S = \left(1- \dfrac{1}{2^2} \right) \left(1- \dfrac{1}{3^2} \right) \left(1- \dfrac{1}{5^2} \right) \left(1- \dfrac{1}{7^2} \right) \ldots$

If the value of the above product $$S$$ can be represented as $$\dfrac{A}{C \pi ^B}$$, where $$A$$, $$B$$ and $$C$$ are positive integers and $$A$$, $$C$$ are coprime to each other, find the value of $$A+B+C$$.

Note: The product is taken over all primes, starting from $$2,3,5,7,\ldots$$.

You may want to look up the Euler product formula to help you with this problem.

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