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.