Primality proof for n = 165310801:
Take b = 2.
b^(n-1) mod n = 1.
397 is prime.
b^((n-1)/397)-1 mod n = 49624731, which is a unit, inverse 92192976.
347 is prime.
b^((n-1)/347)-1 mod n = 128970448, which is a unit, inverse 133210330.
(347 * 397) divides n-1.
(347 * 397)^2 > n.
n is prime by Pocklington's theorem.