Primality proof for n = 26889041:
Take b = 2.
b^(n-1) mod n = 1.
336113 is prime. b^((n-1)/336113)-1 mod n = 15328821, which is a unit, inverse 13939937.
(336113) divides n-1.
(336113)^2 > n.
n is prime by Pocklington's theorem.