Primality proof for n = 8761:
Take b = 2.
b^(n-1) mod n = 1.
73 is prime.
b^((n-1)/73)-1 mod n = 7302, which is a unit, inverse 2504.
5 is prime.
b^((n-1)/5)-1 mod n = 239, which is a unit, inverse 5022.
(5 * 73) divides n-1.
(5 * 73)^2 > n.
n is prime by Pocklington's theorem.