Primality proof for n = 1241450905117:
Take b = 2.
b^(n-1) mod n = 1.
29822497 is prime.
b^((n-1)/29822497)-1 mod n = 423251257161, which is a unit, inverse 736755591818.
(29822497) divides n-1.
(29822497)^2 > n.
n is prime by Pocklington's theorem.