Primality proof for n = 2412961:
Take b = 2.
b^(n-1) mod n = 1.
457 is prime.
b^((n-1)/457)-1 mod n = 1574612, which is a unit, inverse 1978403.
11 is prime.
b^((n-1)/11)-1 mod n = 970484, which is a unit, inverse 1436321.
(11 * 457) divides n-1.
(11 * 457)^2 > n.
n is prime by Pocklington's theorem.