Primality proof for n = 1176035613847:
Take b = 2.
b^(n-1) mod n = 1.
103393 is prime.
b^((n-1)/103393)-1 mod n = 675688275371, which is a unit, inverse 1034661117117.
25969 is prime.
b^((n-1)/25969)-1 mod n = 901972567670, which is a unit, inverse 254810059669.
(25969 * 103393) divides n-1.
(25969 * 103393)^2 > n.
n is prime by Pocklington's theorem.