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.