Primality proof for n = 7349:

Take b = 2.

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

167 is prime.
b^((n-1)/167)-1 mod n = 5654, which is a unit, inverse 4288.

(167) divides n-1.

(167)^2 > n.

n is prime by Pocklington's theorem.