Primality proof for n = 165437:

Take b = 2.

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

701 is prime.
b^((n-1)/701)-1 mod n = 11880, which is a unit, inverse 124593.

(701) divides n-1.

(701)^2 > n.

n is prime by Pocklington's theorem.