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.