Primality proof for n = 1495199339761412565498084319:

Take b = 2.

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

426632512014427833817 is prime.
b^((n-1)/426632512014427833817)-1 mod n = 748955878985560809754141106, which is a unit, inverse 166870529054719175605931730.

(426632512014427833817) divides n-1.

(426632512014427833817)^2 > n.

n is prime by Pocklington's theorem.