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.