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.