Primality proof for n = 165703:

Take b = 2.

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

27617 is prime.
b^((n-1)/27617)-1 mod n = 63, which is a unit, inverse 76276.

(27617) divides n-1.

(27617)^2 > n.

n is prime by Pocklington's theorem.