Primality proof for n = 64817:

Take b = 2.

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

4051 is prime.
b^((n-1)/4051)-1 mod n = 718, which is a unit, inverse 39811.

(4051) divides n-1.

(4051)^2 > n.

n is prime by Pocklington's theorem.