Primality proof for n = 142183:
Take b = 2.
b^(n-1) mod n = 1.
2633 is prime. b^((n-1)/2633)-1 mod n = 44863, which is a unit, inverse 140966.
(2633) divides n-1.
(2633)^2 > n.
n is prime by Pocklington's theorem.