Primality proof for n = 21407:

Take b = 2.

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

139 is prime.
b^((n-1)/139)-1 mod n = 35, which is a unit, inverse 16514.

11 is prime.
b^((n-1)/11)-1 mod n = 15567, which is a unit, inverse 15773.

(11 * 139) divides n-1.

(11 * 139)^2 > n.

n is prime by Pocklington's theorem.