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

Probability Level 3

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 $a+b$ .