Primality proof for n = 19920925890426226515689032734344471:

Take b = 2.

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

1632500449985791 is prime.
b^((n-1)/1632500449985791)-1 mod n = 14093731092224632980825067375814556, which is a unit, inverse 19370752468304835148074963681665270.

4310859807493 is prime.
b^((n-1)/4310859807493)-1 mod n = 12405873217136715948481698156536157, which is a unit, inverse 3777502599179378996957533529262410.

(4310859807493 * 1632500449985791) divides n-1.

(4310859807493 * 1632500449985791)^2 > n.

n is prime by Pocklington's theorem.