## Counting primitive Pythagorean triples

### Problem 540

A **Pythagorean triple** consists of three positive integers $a, b$ and $c$ satisfying $a^2+b^2=c^2$.

The triple is called primitive if $a, b$ and $c$ are relatively prime.

Let P($n$) be the number of **primitive Pythagorean triples** with $a < b < c \le n$.

For example P(20) = 3, since there are three triples: (3,4,5), (5,12,13) and (8,15,17).

You are given that P(10^{6}) = 159139.

Find P(3141592653589793).