If you check the section "Extensions of the standard dictionary numbers" on the page you linked, there's a system for naming arbitrarily large numbers as -illio

If you check the section "Extensions of the standard dictionary numbers" on the page you linked, there's a system for naming arbitrarily large numbers as -illions. The prime here is approx. 8.82 * 10^41024319, and 10^41024319 is the 13674772nd -illion (short scale), so it would begin eight tredecilliquattuorseptuagintasescentilliduoseptuagintaseptingentillion.