Primality proof for n = 426050702417:
Take b = 2.
b^(n-1) mod n = 1.
4098533 is prime. b^((n-1)/4098533)-1 mod n = 366235129210, which is a unit, inverse 311837701406.
(4098533) divides n-1.
(4098533)^2 > n.
n is prime by Pocklington's theorem.