Primality proof for n = 255515944373312847190720520512484175977:

Take b = 2.

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

107590001 is prime.
b^((n-1)/107590001)-1 mod n = 82381214149343919061612748413412685902, which is a unit, inverse 235081362755335172132203715226758066727.

7240687 is prime.
b^((n-1)/7240687)-1 mod n = 111233916942653821000329437866037388563, which is a unit, inverse 175544394104025381149509263364095140941.

96557 is prime.
b^((n-1)/96557)-1 mod n = 47418180093458530687350227428022525795, which is a unit, inverse 52333299885033245219942804006191421971.

(96557 * 7240687 * 107590001) divides n-1.

(96557 * 7240687 * 107590001)^2 > n.

n is prime by Pocklington's theorem.