Primality proof for n = 55516481:

Take b = 2.

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

397 is prime.
b^((n-1)/397)-1 mod n = 21072120, which is a unit, inverse 47286639.

23 is prime.
b^((n-1)/23)-1 mod n = 39987660, which is a unit, inverse 43750573.

(23 * 397) divides n-1.

(23 * 397)^2 > n.

n is prime by Pocklington's theorem.