Primality proof for n = 188353237:
<p>Take b = 2.
<p>b^(n-1) mod n = 1.
<p><a href=1613.html>1613 is prime.</a>
<br>b^((n-1)/1613)-1 mod n = 37935592, which is a unit, inverse 82301414.
<p><a href=263.html>263 is prime.</a>
<br>b^((n-1)/263)-1 mod n = 173728644, which is a unit, inverse 125789862.
<p>(263 * 1613) divides n-1.
<p>(263 * 1613)^2 > n.
<p>n is prime by Pocklington's theorem.