Primality proof for n = 121283:
Take b = 2.
b^(n-1) mod n = 1.
8663 is prime. b^((n-1)/8663)-1 mod n = 16383, which is a unit, inverse 17397.
(8663) divides n-1.
(8663)^2 > n.
n is prime by Pocklington's theorem.