Primality proof for n = 1157184950641651:

Take b = 2.

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

377554267 is prime.
b^((n-1)/377554267)-1 mod n = 790295379323137, which is a unit, inverse 312286053323046.

(377554267) divides n-1.

(377554267)^2 > n.

n is prime by Pocklington's theorem.