Primality proof for n = 3067692486481841:

Take b = 2.

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

2412961 is prime.
b^((n-1)/2412961)-1 mod n = 74457826022028, which is a unit, inverse 644128333937056.

2270249 is prime.
b^((n-1)/2270249)-1 mod n = 836664485586621, which is a unit, inverse 2943912388976040.

(2270249 * 2412961) divides n-1.

(2270249 * 2412961)^2 > n.

n is prime by Pocklington's theorem.