Primality proof for n = 5481473:
Take b = 2.
b^(n-1) mod n = 1.
101 is prime.
b^((n-1)/101)-1 mod n = 1821509, which is a unit, inverse 4523687.
53 is prime.
b^((n-1)/53)-1 mod n = 545983, which is a unit, inverse 2270545.
(53 * 101) divides n-1.
(53 * 101)^2 > n.
n is prime by Pocklington's theorem.