Primality proof for n = 28800823:

Take b = 2.

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

757 is prime.
b^((n-1)/757)-1 mod n = 20738982, which is a unit, inverse 14680532.

373 is prime.
b^((n-1)/373)-1 mod n = 1291123, which is a unit, inverse 17692951.

(373 * 757) divides n-1.

(373 * 757)^2 > n.

n is prime by Pocklington's theorem.