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.