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.