Primality proof for n = 419:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=19.html>19 is prime.</a>
<br>b^((n-1)/19)-1 mod n = 113, which is a unit, inverse 89.
<p><a href=11.html>11 is prime.</a>
<br>b^((n-1)/11)-1 mod n = 333, which is a unit, inverse 190.
<p>(11 * 19) divides n-1.
<p>(11 * 19)^2 > n.
<p>n is prime by Pocklington's theorem.