Primality proof for n = 163027:

Take b = 2.

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

3019 is prime.
b^((n-1)/3019)-1 mod n = 21839, which is a unit, inverse 73261.

(3019) divides n-1.

(3019)^2 > n.

n is prime by Pocklington's theorem.