We consider the virial coefficients of an idealized model polymer under good solvent conditions, the so-called pearl-necklace model, consisting of a fully flexible chain of m tangent hard spheres. We employ an efficient algorithm recently proposed to determine the second, third, and fourth virial coefficients of chains of up to 100 monomers. We also include some preliminary results for chains of up to 200 monomers. These results, which include the first off-lattice calculations of third and fourth virial coefficients of polymer models, are compared with predictions obtained from Wertheim's equation of state. It is shown that, despite the good agreement of Wertheim's equation of state for the compressibility factor, the predictions for the individual virial coefficients are far from satisfactory. It it shown that for the values of m considered in this work, the truncated virial expansion correctly describes the equation of state up to packing fractions of 0.25. A new equation of state which describes the low and high density regimes of the pearl-necklace model is proposed.