\({a, b, c}\) is a Primary Pythagorean Triple (PPT) when: \({a}^{2}+{b}^{2}={c}^{2}\), \({a, b, c} \in \mathbb{Z}\), and \({a, b, c}\) are relatively prime.

Ex. \({3, 4, 5}\) is a PPT while \({6, 8, 10}\) isn't.

How many PPTs are there where \(a, b, c\leq 1000\)?

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