Break It Down

4ab2=c\large 4^{a}-b^{2}=c

There are a finite number of ordered triples (a,b,c)(a,b,c) that can satisfy the above equation, where a,b,a,b, and cc 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)(4,5,6), (4,6,8), then the answer would be 4+5+6+8=23.4+5+6+8=23.

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

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