Primality proof for n = 72106336199:

Take b = 2.

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

2773320623 is prime.
b^((n-1)/2773320623)-1 mod n = 67108863, which is a unit, inverse 8149528284.

(2773320623) divides n-1.

(2773320623)^2 > n.

n is prime by Pocklington's theorem.