Take b = 2.

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

12527 is prime.

b^((n-1)/12527)-1 mod n = 1065496752, which is a unit, inverse 584671775.

487 is prime.

b^((n-1)/487)-1 mod n = 989411564, which is a unit, inverse 922745957.

(487 * 12527) divides n-1.

(487 * 12527)^2 > n.

n is prime by Pocklington's theorem.