Considering the formula for the area of the triangle
if the semi-perimeter is a prime, p, then the largest possible power of p in the product of
is one, because (s - a), (s - b), and (s - c) must all be smaller than s = p and because s is prime they cannot be factors. This means that the area must involve some number times the square root of p, which cannot be rational if p is prime. Therefore all integral triangles have a semi-perimeter that is a composite number.