G.284 prime number prime — Heath

VII.29

Any prime number is prime to any number which it does not measure.

Let A be a prime number, and let it not measure B;

I say that B, A are prime to one another.

For, if B, A are not prime to one another, some number will measure them.

Let C measure them.

Since C measures B, and A does not measure B,

therefore C is not the same with A.

Now, since C measures B, A,

therefore it also measures A which is prime, though it is not the same with it : which is impossible.

Therefore no number will measure B, A.

Therefore A, B are prime to one another.

Q. E. D.

Dependency Graph

Required for

G.285, G.342, G.343, G.344, G.364, G.370