Primality proof for n = 26979779:
Take b = 2.
b^(n-1) mod n = 1.
26399 is prime. b^((n-1)/26399)-1 mod n = 11632, which is a unit, inverse 9808931.
(26399) divides n-1.
(26399)^2 > n.
n is prime by Pocklington's theorem.