Primality proof for n = 41:
Take b = 3.
b^(n-1) mod n = 1.
2 is prime. b^((n-1)/2)-1 mod n = 39, which is a unit, inverse 20.
(2^3) divides n-1.
(2^3)^2 > n.
n is prime by Pocklington's theorem.