Primality proof for n = 7240687:

Take b = 2.

b^(n-1) mod n = 1.

1206781 is prime.
b^((n-1)/1206781)-1 mod n = 63, which is a unit, inverse 5746577.

(1206781) divides n-1.

(1206781)^2 > n.

n is prime by Pocklington's theorem.