Primality proof for n = 21347:

Take b = 2.

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

821 is prime.
b^((n-1)/821)-1 mod n = 15242, which is a unit, inverse 10413.

(821) divides n-1.

(821)^2 > n.

n is prime by Pocklington's theorem.