Primality proof for n = 97151:

Take b = 2.

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

67 is prime.
b^((n-1)/67)-1 mod n = 16208, which is a unit, inverse 43067.

29 is prime.
b^((n-1)/29)-1 mod n = 45322, which is a unit, inverse 95867.

(29 * 67) divides n-1.

(29 * 67)^2 > n.

n is prime by Pocklington's theorem.