Primality proof for n = 1531:
Take b = 2.
b^(n-1) mod n = 1.
17 is prime.
b^((n-1)/17)-1 mod n = 501, which is a unit, inverse 492.
5 is prime.
b^((n-1)/5)-1 mod n = 224, which is a unit, inverse 745.
(5 * 17) divides n-1.
(5 * 17)^2 > n.
n is prime by Pocklington's theorem.