Primality proof for n = 65147:
Take b = 2.
b^(n-1) mod n = 1.
32573 is prime. b^((n-1)/32573)-1 mod n = 3, which is a unit, inverse 21716.
(32573) divides n-1.
(32573)^2 > n.
n is prime by Pocklington's theorem.