  In the $N$-body problem, a simple choreography is a periodic solution, where
all masses chase each other on a single loop. In this paper we prove that for
the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are
at least $2^{N-3} + 2^{[(N-3)/2]}$ different main simple choreographies. This
confirms a conjecture given by Chenciner and etc. in \cite{CGMS02}.
