Primality proof for n = 21384809:

Take b = 2.

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

11987 is prime.
b^((n-1)/11987)-1 mod n = 19585778, which is a unit, inverse 9302612.

(11987) divides n-1.

(11987)^2 > n.

n is prime by Pocklington's theorem.