The cross sections for 59, 60Ca, recently measured in the 345 A MeV reaction, were estimated using the FRACS parametrization and an empirical formula, which are in good agreement. The FRACS parametrization and the empirical formula are combined to predict the cross sections for extreme calcium isotopes in the reactions at the incident energies of 60, 80, and 345 A MeV. The dependence of emperical formula parameters on the reaction system, as well as the incident energy, are discussed. The results indicate that can be discovered in reactions of 60, 80 A MeV . The predicted binding energy for extreme neutron-rich isotopes by the spherical relativistic continuum Hartree-Bogoliubov theory was adopted in the calculation. Hence, the planned Beijing Isotope-Separation-On Line Neutron-Rich Beam Facility (BISOL), which is a third generation radioactive ion beam facility, could provide the opportunity to discover and neighboring neutron-drip line nuclei.