Primality proof for n = 61681:

Take b = 3.

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

257 is prime.
b^((n-1)/257)-1 mod n = 28921, which is a unit, inverse 54001.

(257) divides n-1.

(257)^2 > n.

n is prime by Pocklington's theorem.