Primality proof for n = 41597:

Take b = 2.

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

10399 is prime.
b^((n-1)/10399)-1 mod n = 15, which is a unit, inverse 19412.

(10399) divides n-1.

(10399)^2 > n.

n is prime by Pocklington's theorem.