#### Proposition #2:

#### All integral triangles have a semi-perimeter that is a composite
number

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.