  A prime number based parametrization for total neutrino-nucleon cross section
is presented. The method employs the relation between prime numbers and their
indices to reproduce neutrino cross sections for neutrino energies from the
$MeV$ to the $PeV$ regions where experimental data are available. This
prime-index relation provides estimates of the neutrino-nucleon cross sections
valid across many decades of neutrino energy scales. The $PeV$ data are from
the recently published astrophysical $\nu_\mu + \bar \nu_\mu$ rates in the
IceCube detector as well as neutrino-nucleon cross section measurements. A
similar method has been employed for high energy $pp$ cross sections which
explains the $(\ln s)^{2}$ parametrization first proposed by Heisenberg.
