Primality proof for n = 139862065649:

Take b = 2.

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

380059961 is prime.
b^((n-1)/380059961)-1 mod n = 47456737026, which is a unit, inverse 56245882722.

(380059961) divides n-1.

(380059961)^2 > n.

n is prime by Pocklington's theorem.