Primality proof for n = 161998547485626779:

Take b = 2.

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

323116924469 is prime.
b^((n-1)/323116924469)-1 mod n = 39556129250456031, which is a unit, inverse 29313188621828313.

(323116924469) divides n-1.

(323116924469)^2 > n.

n is prime by Pocklington's theorem.