Primality proof for n = 1720805198043061735464389957585107660393:

Take b = 2.

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

548794774797769816735663 is prime.
b^((n-1)/548794774797769816735663)-1 mod n = 1202074940597289010751111877187266371031, which is a unit, inverse 1470144048420718558873948599752682602060.

(548794774797769816735663) divides n-1.

(548794774797769816735663)^2 > n.

n is prime by Pocklington's theorem.