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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