Primes and products

Calculus Level 5

Find $$\displaystyle S=\prod _{ p\ge 2 }^{ \infty }{ (1+\frac { 2 }{ { p }^{ 2 }-1 } ) }$$.

Where $$p$$ is a prime number that is $$p$$ only takes values $$2,3,5,7,11......$$

If $$S$$ can be represented as $$\dfrac{a}{b}$$. Find $$a+b$$

Details and Assumptions

1)$$a,b$$ are coprime positive integers.

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