Primality proof for n = 60509:
Take b = 2.
b^(n-1) mod n = 1.
2161 is prime. b^((n-1)/2161)-1 mod n = 17531, which is a unit, inverse 33442.
(2161) divides n-1.
(2161)^2 > n.
n is prime by Pocklington's theorem.