Primality proof for n = 205115282021455665897114700593932402728804164701536103180137503955397371:

Take b = 2.

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

255515944373312847190720520512484175977 is prime.
b^((n-1)/255515944373312847190720520512484175977)-1 mod n = 53072002638256206696760401718638995221936714922431175139555783581918753, which is a unit, inverse 81475874003799270243122483189086420723726815346591292526890606927317739.

(255515944373312847190720520512484175977) divides n-1.

(255515944373312847190720520512484175977)^2 > n.

n is prime by Pocklington's theorem.