Primality proof for n = 3458867485158836715058751:

Take b = 2.

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

91450740527 is prime.
b^((n-1)/91450740527)-1 mod n = 752412705015615888443755, which is a unit, inverse 2605610309573123537551763.

30257753761 is prime.
b^((n-1)/30257753761)-1 mod n = 721261711735024118171595, which is a unit, inverse 127911383153237679174366.

(30257753761 * 91450740527) divides n-1.

(30257753761 * 91450740527)^2 > n.

n is prime by Pocklington's theorem.