Primality proof for n = 2111:

Take b = 2.

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

211 is prime.
b^((n-1)/211)-1 mod n = 1023, which is a unit, inverse 1364.

(211) divides n-1.

(211)^2 > n.

n is prime by Pocklington's theorem.