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.