Primality proof for n = 361725589517273017:

Take b = 2.

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

674750394557 is prime.
b^((n-1)/674750394557)-1 mod n = 206817309394499643, which is a unit, inverse 184089148017814789.

(674750394557) divides n-1.

(674750394557)^2 > n.

n is prime by Pocklington's theorem.