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.