Primality proof for n = 68521:

Take b = 2.

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

571 is prime.
b^((n-1)/571)-1 mod n = 34861, which is a unit, inverse 36400.

(571) divides n-1.

(571)^2 > n.

n is prime by Pocklington's theorem.