Primality proof for n = 190455129210693390224369129:

Take b = 2.

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

1674656872585139 is prime.
b^((n-1)/1674656872585139)-1 mod n = 37629468049426663660937826, which is a unit, inverse 143247471639072917272623193.

(1674656872585139) divides n-1.

(1674656872585139)^2 > n.

n is prime by Pocklington's theorem.