Primality proof for n = 2857:

Take b = 5.

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

17 is prime.
b^((n-1)/17)-1 mod n = 1740, which is a unit, inverse 1949.

3 is prime.
b^((n-1)/3)-1 mod n = 2505, which is a unit, inverse 2021.

2 is prime.
b^((n-1)/2)-1 mod n = 2855, which is a unit, inverse 1428.

(2^3 * 3 * 17) divides n-1.

(2^3 * 3 * 17)^2 > n.

n is prime by Pocklington's theorem.