Primality proof for n = 221251:
Take b = 2.
b^(n-1) mod n = 1.
59 is prime.
b^((n-1)/59)-1 mod n = 61540, which is a unit, inverse 110550.
5 is prime.
b^((n-1)/5)-1 mod n = 200941, which is a unit, inverse 68968.
(5^4 * 59) divides n-1.
(5^4 * 59)^2 > n.
n is prime by Pocklington's theorem.