Any number is either prime or is measured by some prime
number.

Let *A* be a number.

I say that *A* either is prime or is measured by some prime number.

If now *A* is prime, then that which was proposed is done.

But if it is composite, then some prime number measures it.

Therefore any number either is prime or is measured by some prime number.

Therefore, *any number is either prime or is measured by some prime
number.*

Q.E.D.