Primality proof for n = 143291:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=89.html>89 is prime.</a>
<br>b^((n-1)/89)-1 mod n = 24661, which is a unit, inverse 9471.
<p><a href=23.html>23 is prime.</a>
<br>b^((n-1)/23)-1 mod n = 82399, which is a unit, inverse 26297.
<p>(23 * 89) divides n-1.
<p>(23 * 89)^2 > n.
<p>n is prime by Pocklington's theorem.