Primality proof for n = 220663:

Take b = 2.

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

41 is prime.
b^((n-1)/41)-1 mod n = 84024, which is a unit, inverse 128812.

23 is prime.
b^((n-1)/23)-1 mod n = 201360, which is a unit, inverse 208557.

(23 * 41) divides n-1.

(23 * 41)^2 > n.

n is prime by Pocklington's theorem.