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.