--description--

Consider the triangles with integer sides $a$, $b$ and $c$ with $a ≤ b ≤ c$.

An integer sided triangle $(a,b,c)$ is called primitive if $gcd(a,b,c) = 1$.

How many primitive integer sided triangles exist with a perimeter not exceeding $10\,000\,000$?

--hints--

primitiveTriangles() should return 5777137137739633000.

assert.strictEqual(primitiveTriangles(), 5777137137739633000);

--seed--

--seed-contents--

function primitiveTriangles() {

  return true;
}

primitiveTriangles();

--solutions--

// solution required