  Pairing plays a central role in nuclear systems. The simplest model for the
pairing is the constant-pairing Hamiltonian. The aim of the present paper is to
include the continuum single particle level density in the constant pairing
Hamiltonian and to make a comparison between the approximate BCS and the exact
Richardson solutions. The continuum is introduced by using the continuum single
particle level density. It is shown that the continuum makes an important
contribution to the pairing parameter even in those case when the continuum is
weakly populated. It is shown that while the approximate BCS solution depends
on the model space the exact Richardson solution does not.
