Primality proof for n = 837116414630376960702915782614178937699338555837:

Take b = 2.

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

1758043857162342261873808298370022542631 is prime.
b^((n-1)/1758043857162342261873808298370022542631)-1 mod n = 125957735572085366797438492604978781274603709635, which is a unit, inverse 317705914156177198993441279189860772521796604582.

(1758043857162342261873808298370022542631) divides n-1.

(1758043857162342261873808298370022542631)^2 > n.

n is prime by Pocklington's theorem.