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.