Primes and products

Calculus Level 5

Find S=p2(1+2p21)\displaystyle S=\prod _{ p\ge 2 }^{ \infty }{ (1+\frac { 2 }{ { p }^{ 2 }-1 } ) } .

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

If SS can be represented as ab\dfrac{a}{b}. Find a+ba+b

Details and Assumptions

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

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