Primality proof for n = 541:
Take b = 2.
b^(n-1) mod n = 1.
5 is prime.
b^((n-1)/5)-1 mod n = 47, which is a unit, inverse 518.
3 is prime.
b^((n-1)/3)-1 mod n = 128, which is a unit, inverse 317.
(3^3 * 5) divides n-1.
(3^3 * 5)^2 > n.
n is prime by Pocklington's theorem.