Primality proof for n = 550480097:

Take b = 2.

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

431 is prime.
b^((n-1)/431)-1 mod n = 366379788, which is a unit, inverse 11781253.

239 is prime.
b^((n-1)/239)-1 mod n = 494142381, which is a unit, inverse 182863584.

(239 * 431) divides n-1.

(239 * 431)^2 > n.

n is prime by Pocklington's theorem.