Primality proof for n = 532731547:

Take b = 2.

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

13721 is prime.
b^((n-1)/13721)-1 mod n = 386709404, which is a unit, inverse 260196056.

719 is prime.
b^((n-1)/719)-1 mod n = 20762579, which is a unit, inverse 219175175.

(719 * 13721) divides n-1.

(719 * 13721)^2 > n.

n is prime by Pocklington's theorem.