# 9109

This number is a prime.

Just showing those entries submitted by 'Keith': (Click here to show all)

Mark n points on a circle and connect every pair of points
with a line, then count the number of regions (r) into
which the interior of the circle is divided. It is a
theorem that if the points on the circle are chosen such
that no three lines intersect at the same point inside the
circle, the total number of regions will be maximized, so
assume this condition holds. As an example, the diagram
below shows that when n=5 there are r=16 regions. Is it
possible for both n and r to be prime? Yes, and aside from
the somewhat trivial case n=2 and r=2 the smallest such
configuration has 23 points and 9109 regions. The next one
after that is n=73, r=1091059.

[Keith]