Primality proof for n = 96557:

Take b = 2.

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

239 is prime.
b^((n-1)/239)-1 mod n = 29585, which is a unit, inverse 8329.

101 is prime.
b^((n-1)/101)-1 mod n = 63064, which is a unit, inverse 50445.

(101 * 239) divides n-1.

(101 * 239)^2 > n.

n is prime by Pocklington's theorem.