Pythagorean triples

A Pythagorean triple is defined as three positive integers $(a,b,c)$ where $a\leq b\leq c$, and $a^{2}+b^{2}=c^{2}.$ They are called primitive triples if $a,b,c$ are coprime. Each triple form the length of the sides of a right triangle, whose perimeter is $P=a+b+c$.

Pythagorean triples is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Task

How many Pythagorean triples are there with a perimeter no larger than 100? Of these, how many are primitive?

Extra: Can your program handle a max perimeter of 1,000,000? What about 10,000,000? 100,000,000?