Using a realistic united-atom force field, molecular dynamics simulations were performed to study homogeneous nucleation of the crystal phase at about 3096 supercooling from the melts of n-pentacontahectane (C150) and a linear polyethylene (C1000), both of which are long enough to exhibit the chain folding that is characteristic of polymer crystallization. The nucleation rate was calculated and the critical nuclei were identified using a mean first-passage time analysis. The nucleation rate was found to be insensitive to the chain length in this range of molecular weight. The critical nucleus, contains about 150 carbons on average and is significantly smaller than the radius of gyration of the chains, at this supercooling. A cylinder model was used to characterize the shape of the crystal nuclei and to calculate the interfacial free energies. A chain segment analysis was performed to characterize the topology of the crystal surface in terms of loops (including folds) and tails. The length distribution of loops is broad, supporting the "switchboard model" for the early stage crystals formed at deep supercooling. Using the survival probability method, the critical nucleus size was determined as a function of temperature. The interfacial free energies were found to be temperature-dependent. The free energy barrier and nucleation rate as functions of temperature were also calculated an compare favorably with experiments.