# Break It Down

$\large 4^{a}-b^{2}=c$

There are a finite number of ordered triples $$(a,b,c)$$ that can satisfy the above equation, where $$a,b,$$ and $$c$$ are all primes.

Find the sum of all distinct primes that are a part of a solution set for the above equation.

 Details and Assumptions:

• If the two solutions were $$(4,5,6), (4,6,8)$$, then the answer would be $$4+5+6+8=23.$$

• $$1$$ is $${\color{red} \text{not}}$$ a prime number.

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