Primality proof for n = 241601:
Take b = 2.
b^(n-1) mod n = 1.
151 is prime.
b^((n-1)/151)-1 mod n = 82141, which is a unit, inverse 230027.
5 is prime.
b^((n-1)/5)-1 mod n = 61938, which is a unit, inverse 19757.
(5^2 * 151) divides n-1.
(5^2 * 151)^2 > n.
n is prime by Pocklington's theorem.