Primality proof for n = 1254043595354617963043866617659:

Take b = 2.

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

14334859726775219 is prime.
b^((n-1)/14334859726775219)-1 mod n = 648270687468679223755191115104, which is a unit, inverse 481001945969039870230636624587.

(14334859726775219) divides n-1.

(14334859726775219)^2 > n.

n is prime by Pocklington's theorem.