Primality proof for n = 29862490908791:

Take b = 2.

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

78591707 is prime.
b^((n-1)/78591707)-1 mod n = 20333071398908, which is a unit, inverse 10344979110248.

(78591707) divides n-1.

(78591707)^2 > n.

n is prime by Pocklington's theorem.