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.