Primality proof for n = 211:
Take b = 2.
b^(n-1) mod n = 1.
7 is prime.
b^((n-1)/7)-1 mod n = 170, which is a unit, inverse 36.
5 is prime.
b^((n-1)/5)-1 mod n = 106, which is a unit, inverse 2.
(5 * 7) divides n-1.
(5 * 7)^2 > n.
n is prime by Pocklington's theorem.