Primality proof for n = 15661:
Take b = 2.
b^(n-1) mod n = 1.
29 is prime.
b^((n-1)/29)-1 mod n = 11485, which is a unit, inverse 3919.
5 is prime.
b^((n-1)/5)-1 mod n = 6623, which is a unit, inverse 5363.
(5 * 29) divides n-1.
(5 * 29)^2 > n.
n is prime by Pocklington's theorem.