Primality proof for n = 5994341377:

Take b = 2.

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

4657 is prime.
b^((n-1)/4657)-1 mod n = 3974926620, which is a unit, inverse 783419215.

419 is prime.
b^((n-1)/419)-1 mod n = 1263804740, which is a unit, inverse 4284275874.

(419 * 4657) divides n-1.

(419 * 4657)^2 > n.

n is prime by Pocklington's theorem.