Primality proof for n = 7156907:
Take b = 2.
b^(n-1) mod n = 1.
3578453 is prime. b^((n-1)/3578453)-1 mod n = 3, which is a unit, inverse 2385636.
(3578453) divides n-1.
(3578453)^2 > n.
n is prime by Pocklington's theorem.