The first 13 prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41

Each of the first thirteen prime numbers is written on an individual piece of paper and put in a box.

If 2 pieces of paper are drawn without replacement, what is the probability that the sum of the 2 numbers will be a prime number?

If the probability can be expressed as \(\dfrac ab\) for coprime positive integers \(a\) and \(b\), find the value of \(a+b\).

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