Primality proof for n = 18127247:
Take b = 2.
b^(n-1) mod n = 1.
9063623 is prime. b^((n-1)/9063623)-1 mod n = 3, which is a unit, inverse 6042416.
(9063623) divides n-1.
(9063623)^2 > n.
n is prime by Pocklington's theorem.