Primality proof for n = 41081:
Take b = 2.
b^(n-1) mod n = 1.
79 is prime.
b^((n-1)/79)-1 mod n = 6276, which is a unit, inverse 10807.
13 is prime.
b^((n-1)/13)-1 mod n = 32464, which is a unit, inverse 20438.
(13 * 79) divides n-1.
(13 * 79)^2 > n.
n is prime by Pocklington's theorem.