Primality proof for n = 23658857317:

Take b = 2.

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

26161 is prime.
b^((n-1)/26161)-1 mod n = 16803971451, which is a unit, inverse 10695012478.

25121 is prime.
b^((n-1)/25121)-1 mod n = 19676504053, which is a unit, inverse 19461089698.

(25121 * 26161) divides n-1.

(25121 * 26161)^2 > n.

n is prime by Pocklington's theorem.