Primality proof for n = 1131014973702835376677:

Take b = 2.

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

39850487891 is prime.
b^((n-1)/39850487891)-1 mod n = 1028016623892686332003, which is a unit, inverse 381895526614639260191.

(39850487891) divides n-1.

(39850487891)^2 > n.

n is prime by Pocklington's theorem.