Primality proof for n = 260441:
Take b = 2.
b^(n-1) mod n = 1.
383 is prime.
b^((n-1)/383)-1 mod n = 201106, which is a unit, inverse 44600.
17 is prime.
b^((n-1)/17)-1 mod n = 234875, which is a unit, inverse 11603.
(17 * 383) divides n-1.
(17 * 383)^2 > n.
n is prime by Pocklington's theorem.