Primality proof for n = 62383:

Take b = 2.

b^(n-1) mod n = 1.

281 is prime.
b^((n-1)/281)-1 mod n = 17735, which is a unit, inverse 55552.

(281) divides n-1.

(281)^2 > n.

n is prime by Pocklington's theorem.