Primality proof for n = 1283159:

Take b = 2.

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

641579 is prime.
b^((n-1)/641579)-1 mod n = 3, which is a unit, inverse 427720.

(641579) divides n-1.

(641579)^2 > n.

n is prime by Pocklington's theorem.