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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