Primality proof for n = 3009341:
Take b = 2.
b^(n-1) mod n = 1.
167 is prime.
b^((n-1)/167)-1 mod n = 1986342, which is a unit, inverse 221100.
53 is prime.
b^((n-1)/53)-1 mod n = 2027033, which is a unit, inverse 1498234.
(53 * 167) divides n-1.
(53 * 167)^2 > n.
n is prime by Pocklington's theorem.