Primality proof for n = 1740482054401:

Take b = 2.

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

127139 is prime.
b^((n-1)/127139)-1 mod n = 1394778125770, which is a unit, inverse 931889182908.

31 is prime.
b^((n-1)/31)-1 mod n = 728278689886, which is a unit, inverse 762457334809.

(31 * 127139) divides n-1.

(31 * 127139)^2 > n.

n is prime by Pocklington's theorem.