Primality proof for n = 15083:
Take b = 2.
b^(n-1) mod n = 1.
7541 is prime. b^((n-1)/7541)-1 mod n = 3, which is a unit, inverse 5028.
(7541) divides n-1.
(7541)^2 > n.
n is prime by Pocklington's theorem.