Primality proof for n = 160847769765829662053086933326768494988741892623088564991:

Take b = 2.

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

1720805198043061735464389957585107660393 is prime.
b^((n-1)/1720805198043061735464389957585107660393)-1 mod n = 133314722030314324150405802053168784648735813247464414252, which is a unit, inverse 98412961777216792508454000380068898757500520055406108187.

(1720805198043061735464389957585107660393) divides n-1.

(1720805198043061735464389957585107660393)^2 > n.

n is prime by Pocklington's theorem.