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Primitive Triangles

Problem 276 Published on Friday, 29th January 2010, 09:00 pm; Solved by 875;
Difficulty rating: 75%

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?