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.