Primitive Triangles

Consider the triangles with integer sides $a$ , $b$ and $c$ with $a \leq b \leq c$ .
An integer sided triangle $(a, b, c)$ is called primitive if $gcd (a, b, c)$ $gcd (a, b, c) = gcd (a, gcd (b, c))$ $= 1$ .
How many primitive integer sided triangles exist with a perimeter not exceeding $10 000 000$ ?

Write-up coming later

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