Primality proof for n = 153259:
<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 = 143377, which is a unit, inverse 100141.
<p><a href=41.html>41 is prime.</a>
<br>b^((n-1)/41)-1 mod n = 153016, which is a unit, inverse 138753.
<p>(41 * 89) divides n-1.
<p>(41 * 89)^2 > n.
<p>n is prime by Pocklington's theorem.