Primality proof for n = 298407043007230668716584089637:

Take b = 2.

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

5924666185313169299 is prime.
b^((n-1)/5924666185313169299)-1 mod n = 199777376438514578804965374316, which is a unit, inverse 155904965922011319053954941227.

(5924666185313169299) divides n-1.

(5924666185313169299)^2 > n.

n is prime by Pocklington's theorem.