Primality proof for n = 201439234573737379:

Take b = 2.

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

718558435081 is prime.
b^((n-1)/718558435081)-1 mod n = 85787672788856600, which is a unit, inverse 182197309422129423.

(718558435081) divides n-1.

(718558435081)^2 > n.

n is prime by Pocklington's theorem.