Primality proof for n = 1512421:

Take b = 2.

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

277 is prime.
b^((n-1)/277)-1 mod n = 1384168, which is a unit, inverse 1214767.

13 is prime.
b^((n-1)/13)-1 mod n = 944448, which is a unit, inverse 1388338.

(13 * 277) divides n-1.

(13 * 277)^2 > n.

n is prime by Pocklington's theorem.