Primality proof for n = 738482592425650221847703733566702107:

Take b = 2.

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

79008864392262625810043 is prime.
b^((n-1)/79008864392262625810043)-1 mod n = 689096227900961313240199558771301689, which is a unit, inverse 409318045992455339257042350588882603.

(79008864392262625810043) divides n-1.

(79008864392262625810043)^2 > n.

n is prime by Pocklington's theorem.