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.