Primality proof for n = 139759026803824079:

Take b = 2.

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

3286873 is prime.
b^((n-1)/3286873)-1 mod n = 74018298784106547, which is a unit, inverse 94099312063304057.

6131 is prime.
b^((n-1)/6131)-1 mod n = 74639927714532779, which is a unit, inverse 41996677652238246.

(6131 * 3286873) divides n-1.

(6131 * 3286873)^2 > n.

n is prime by Pocklington's theorem.