Primality proof for n = 96893:
Take b = 2.
b^(n-1) mod n = 1.
24223 is prime. b^((n-1)/24223)-1 mod n = 15, which is a unit, inverse 83974.
(24223) divides n-1.
(24223)^2 > n.
n is prime by Pocklington's theorem.