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.