Primality proof for n = 522528103:
Take b = 2.
b^(n-1) mod n = 1.
21143 is prime.
b^((n-1)/21143)-1 mod n = 196245148, which is a unit, inverse 504004310.
1373 is prime.
b^((n-1)/1373)-1 mod n = 880858, which is a unit, inverse 344921177.
(1373 * 21143) divides n-1.
(1373 * 21143)^2 > n.
n is prime by Pocklington's theorem.