Primality proof for n = 51473:

Take b = 2.

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

3217 is prime.
b^((n-1)/3217)-1 mod n = 14062, which is a unit, inverse 36403.

(3217) divides n-1.

(3217)^2 > n.

n is prime by Pocklington's theorem.