Primality proof for n = 1255525949:

Take b = 2.

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

116989 is prime.
b^((n-1)/116989)-1 mod n = 806674565, which is a unit, inverse 744224629.

(116989) divides n-1.

(116989)^2 > n.

n is prime by Pocklington's theorem.