Eccoci.

Consider the triangles with integer sides $a$, $b$ and $c$ with $a \le b \le c$.
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 $10\,000\,000$?