Primality proof for n = 2220636239:
Take b = 2.
b^(n-1) mod n = 1.
1110318119 is prime. b^((n-1)/1110318119)-1 mod n = 3, which is a unit, inverse 740212080.
(1110318119) divides n-1.
(1110318119)^2 > n.
n is prime by Pocklington's theorem.