Primality proof for n = 7144903:

Take b = 2.

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

132313 is prime.
b^((n-1)/132313)-1 mod n = 2875257, which is a unit, inverse 5808523.

(132313) divides n-1.

(132313)^2 > n.

n is prime by Pocklington's theorem.