Primality proof for n = 128262069029:
Take b = 2.
b^(n-1) mod n = 1.
1687658803 is prime.
b^((n-1)/1687658803)-1 mod n = 2663518125, which is a unit, inverse 100001539811.
(1687658803) divides n-1.
(1687658803)^2 > n.
n is prime by Pocklington's theorem.