Primality proof for n = 1285908257:

Take b = 2.

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

33797 is prime.
b^((n-1)/33797)-1 mod n = 361465803, which is a unit, inverse 371382902.

41 is prime.
b^((n-1)/41)-1 mod n = 573106111, which is a unit, inverse 1198157725.

(41 * 33797) divides n-1.

(41 * 33797)^2 > n.

n is prime by Pocklington's theorem.