Primality proof for n = 5662229:

Take b = 2.

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

521 is prime.
b^((n-1)/521)-1 mod n = 3212052, which is a unit, inverse 1564518.

19 is prime.
b^((n-1)/19)-1 mod n = 4134036, which is a unit, inverse 3088404.

(19 * 521) divides n-1.

(19 * 521)^2 > n.

n is prime by Pocklington's theorem.