Two-Prime Triples

A Pythagorean triple is a triple of positive integers (x,y,z)(x,y,z) such that x2+y2=z2.x^2+y^2=z^2. Find the sum of all z100z\leq 100, for which there exists a Pythagorean triple (x,y,z)(x,y,z) with exactly two of the numbers xx, yy and zz being prime.

Details and assumptions

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

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