Primality proof for n = 79008864392262625810043:

Take b = 2.

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

39504432196131312905021 is prime.
b^((n-1)/39504432196131312905021)-1 mod n = 3, which is a unit, inverse 26336288130754208603348.

(39504432196131312905021) divides n-1.

(39504432196131312905021)^2 > n.

n is prime by Pocklington's theorem.