No, there are no elements with atomic numbers between two existing elements on the periodic table. The periodic table organizes elements in order of increasing atomic number, which corresponds to the number of protons in the nucleus of an atom. Each element on the periodic table has a unique atomic number, and there are no gaps or missing numbers between them. The periodic table is a comprehensive representation of all known elements, and any new elements discovered in the future will be added to the table in the appropriate positions based on their atomic numbers.