Primality proof for n = 767617:

Take b = 2.

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

1999 is prime.
b^((n-1)/1999)-1 mod n = 425880, which is a unit, inverse 92441.

(1999) divides n-1.

(1999)^2 > n.

n is prime by Pocklington's theorem.