Primality proof for n = 10211:

Take b = 2.

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

1021 is prime.
b^((n-1)/1021)-1 mod n = 1023, which is a unit, inverse 6987.

(1021) divides n-1.

(1021)^2 > n.

n is prime by Pocklington's theorem.