Primality proof for n = 379979:

Take b = 2.

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

189989 is prime.
b^((n-1)/189989)-1 mod n = 3, which is a unit, inverse 126660.

(189989) divides n-1.

(189989)^2 > n.

n is prime by Pocklington's theorem.