Primality proof for n = 26886215762884663:

Take b = 2.

b^(n-1) mod n = 1.

177481 is prime.
b^((n-1)/177481)-1 mod n = 20778900493678294, which is a unit, inverse 249612942564685.

166021 is prime.
b^((n-1)/166021)-1 mod n = 11168744619416036, which is a unit, inverse 12512763224015909.

(166021 * 177481) divides n-1.

(166021 * 177481)^2 > n.

n is prime by Pocklington's theorem.