Primality proof for n = 552833:

Take b = 2.

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

617 is prime.
b^((n-1)/617)-1 mod n = 318030, which is a unit, inverse 27088.

7 is prime.
b^((n-1)/7)-1 mod n = 173656, which is a unit, inverse 113915.

(7 * 617) divides n-1.

(7 * 617)^2 > n.

n is prime by Pocklington's theorem.