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.