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.