Primality proof for n = 43153393:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1069.html>1069 is prime.</a>
<br>b^((n-1)/1069)-1 mod n = 26996680, which is a unit, inverse 10239774.
<p><a href=29.html>29 is prime.</a>
<br>b^((n-1)/29)-1 mod n = 16879145, which is a unit, inverse 8206854.
<p>(29^2 * 1069) divides n-1.
<p>(29^2 * 1069)^2 > n.
<p>n is prime by Pocklington's theorem.