Primality proof for n = 41201:
Take b = 3.
b^(n-1) mod n = 1.
103 is prime.
b^((n-1)/103)-1 mod n = 16838, which is a unit, inverse 17121.
5 is prime.
b^((n-1)/5)-1 mod n = 18548, which is a unit, inverse 26467.
(5^2 * 103) divides n-1.
(5^2 * 103)^2 > n.
n is prime by Pocklington's theorem.