Primality proof for n = 4206583:
Take b = 2.
b^(n-1) mod n = 1.
233 is prime.
b^((n-1)/233)-1 mod n = 2192711, which is a unit, inverse 2712819.
59 is prime.
b^((n-1)/59)-1 mod n = 3747588, which is a unit, inverse 836166.
(59 * 233) divides n-1.
(59 * 233)^2 > n.
n is prime by Pocklington's theorem.