Primality proof for n = 26510263489:

Take b = 2.

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

2707339 is prime.
b^((n-1)/2707339)-1 mod n = 15268174219, which is a unit, inverse 13524403172.

(2707339) divides n-1.

(2707339)^2 > n.

n is prime by Pocklington's theorem.