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.