Primality proof for n = 204451032782023823759:

Take b = 2.

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

49736333249 is prime.
b^((n-1)/49736333249)-1 mod n = 160954841054405487912, which is a unit, inverse 32125116810520615807.

(49736333249) divides n-1.

(49736333249)^2 > n.

n is prime by Pocklington's theorem.