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.