Primality proof for n = 24453091069698428153:

Take b = 2.

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

818488084109 is prime.
b^((n-1)/818488084109)-1 mod n = 8407771661331252268, which is a unit, inverse 5779515667575309546.

(818488084109) divides n-1.

(818488084109)^2 > n.

n is prime by Pocklington's theorem.