Primality proof for n = 79806171026243:

Take b = 2.

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

21258969373 is prime.
b^((n-1)/21258969373)-1 mod n = 3794218842250, which is a unit, inverse 51000527180810.

(21258969373) divides n-1.

(21258969373)^2 > n.

n is prime by Pocklington's theorem.