Primality proof for n = 10061:

Take b = 2.

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

503 is prime.
b^((n-1)/503)-1 mod n = 2231, which is a unit, inverse 7955.

(503) divides n-1.

(503)^2 > n.

n is prime by Pocklington's theorem.