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.