Primality proof for n = 17957:

Take b = 2.

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

67 is prime.
b^((n-1)/67)-1 mod n = 14920, which is a unit, inverse 4269.

(67^2) divides n-1.

(67^2)^2 > n.

n is prime by Pocklington's theorem.