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.