# Two-Prime Triples

A Pythagorean triple is a triple of positive integers $(x,y,z)$ such that $x^2+y^2=z^2.$ Find the sum of all $z\leq 100$, for which there exists a Pythagorean triple $(x,y,z)$ with exactly two of the numbers $x$, $y$ and $z$ being prime.

Details and assumptions

Each distinct value of $z$ should only be included once. For example, $(3, 4, 5)$ and $(4, 3, 5)$ satisfy the conditions, and so $z=5$ is a possible value.

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