  We give a mass formula for computing the mass spectrum of mesons. By this
formula we show that there are many mesons with their masses corresponding to a
prime number. In particular we show that all strange mesons are with their
masses corresponding to a prime number. With these prime numbers indexing the
mesons we give a classification of mesons. We set up a knot model of mesons to
derive this mass formula. In this knot model mesons and their anti-particles
are modeled by knots and their mirror images respectively. Then the amphichiral
knots which are equivalent to their mirror images are used to model mesons
which are identical with their anti-particles. With this knot model we show
that there is a periodic phenomenon in the classification of mesons such that
the starting nonet and the ending nonet are nonets of pseudoscalar mesons with
the $\pi$ meson modeled by an amphichiral knot. From this periodic phenomenon
we give a theoretical argument for the existence of charm-anticharm mesons.
