Primality proof for n = 67153:
Take b = 2.
b^(n-1) mod n = 1.
1399 is prime. b^((n-1)/1399)-1 mod n = 766, which is a unit, inverse 66890.
(1399) divides n-1.
(1399)^2 > n.
n is prime by Pocklington's theorem.