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.