Inspired by Calvin Lin

A primitive pythagorean triplet is a set of three positive integer \( \{ a, b, c \} \) which are mutually prime and satisfy \( a^2 + b^2 = c^2 \).

How many such triplets exist such that \( 1 \leq c \leq 100 \) and none of \(a, b, c \) are prime?

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