Primality proof for n = 1003679:

Take b = 2.

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

38603 is prime.
b^((n-1)/38603)-1 mod n = 866049, which is a unit, inverse 795760.

(38603) divides n-1.

(38603)^2 > n.

n is prime by Pocklington's theorem.