Such Relations, Much Wow!

Number Theory Level 2

Let $$A$$ be the set of all primes which cannot be expressed as $$6p\pm1$$, $$p\in \mathbb{N}$$. Let $$R$$ be a random relation mapping from $$A$$ to itself. The probability that the relation maps all the elements in the domain to all the elements in the co domain is given by $$\frac{a}{b}$$, where $$a,b\in \mathbb{N}$$ and $$g.c.d.(a,b)=1$$. Find $$a+b$$

Details:

The relation is bijective.

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