Primality proof for n = 9349:

Take b = 2.

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

41 is prime.
b^((n-1)/41)-1 mod n = 1994, which is a unit, inverse 7422.

19 is prime.
b^((n-1)/19)-1 mod n = 4422, which is a unit, inverse 1444.

(19 * 41) divides n-1.

(19 * 41)^2 > n.

n is prime by Pocklington's theorem.