Primality proof for n = 51481:
Take b = 3.
b^(n-1) mod n = 1.
13 is prime.
b^((n-1)/13)-1 mod n = 48873, which is a unit, inverse 3336.
11 is prime.
b^((n-1)/11)-1 mod n = 31686, which is a unit, inverse 34566.
5 is prime.
b^((n-1)/5)-1 mod n = 47886, which is a unit, inverse 6888.
(5 * 11 * 13) divides n-1.
(5 * 11 * 13)^2 > n.
n is prime by Pocklington's theorem.