Primality proof for n = 409891:
Take b = 3.
b^(n-1) mod n = 1.
1051 is prime. b^((n-1)/1051)-1 mod n = 183629, which is a unit, inverse 405353.
(1051) divides n-1.
(1051)^2 > n.
n is prime by Pocklington's theorem.