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.