Primality proof for n = 189989:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=47497.html>47497 is prime.</a>
<br>b^((n-1)/47497)-1 mod n = 15, which is a unit, inverse 12666.
<p>(47497) divides n-1.
<p>(47497)^2 > n.
<p>n is prime by Pocklington's theorem.