Primality proof for n = 1424961889141606181:

Take b = 2.

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

7959649 is prime.
b^((n-1)/7959649)-1 mod n = 1342969993534657940, which is a unit, inverse 340802350814694891.

58481 is prime.
b^((n-1)/58481)-1 mod n = 1057125979828876387, which is a unit, inverse 813073097731928778.

(58481 * 7959649) divides n-1.

(58481 * 7959649)^2 > n.

n is prime by Pocklington's theorem.