Primality proof for n = 10957:
Take b = 2.
b^(n-1) mod n = 1.
83 is prime.
b^((n-1)/83)-1 mod n = 1834, which is a unit, inverse 10724.
11 is prime.
b^((n-1)/11)-1 mod n = 10438, which is a unit, inverse 7368.
(11 * 83) divides n-1.
(11 * 83)^2 > n.
n is prime by Pocklington's theorem.