Primality proof for n = 4211:

Take b = 2.

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

421 is prime.
b^((n-1)/421)-1 mod n = 1023, which is a unit, inverse 2017.

(421) divides n-1.

(421)^2 > n.

n is prime by Pocklington's theorem.