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 $P(3141592653589793)$.