Primality proof for n = 203333173:

Take b = 2.

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

2420633 is prime.
b^((n-1)/2420633)-1 mod n = 125851850, which is a unit, inverse 113605773.

(2420633) divides n-1.

(2420633)^2 > n.

n is prime by Pocklington's theorem.