Primality proof for n = 379795560371:
Take b = 2.
b^(n-1) mod n = 1.
18413 is prime.
b^((n-1)/18413)-1 mod n = 306896679354, which is a unit, inverse 242678902243.
1583 is prime.
b^((n-1)/1583)-1 mod n = 173019972171, which is a unit, inverse 272941825608.
(1583 * 18413) divides n-1.
(1583 * 18413)^2 > n.
n is prime by Pocklington's theorem.