What is the oldest Irish surname in Ireland?

The oldest Irish surname in Ireland is considered to be O Cleirigh or O'Clery, also O'Conor or O'Connor, with O Cleirigh dating to 10th century, and O'Clery being one of earliest hereditary surnames in Europe, though several Irish surnames claim oldest status. Irish surnames began as hereditary surnames in 10th and 11th centuries, earlier than most European surnames, with Irish being first to use hereditary surnames. Oldest Irish surname is often cited as O Cleirigh, meaning descendant of Cleireach, with history dating to 974 AD, with family of scholars and historians in Donegal, or O'Conor from Conor, with O'Conor family dating to 10th century, Kings of Connacht. Other claimants include O'Neill, O'Brien, O'Sullivan, all ancient Gaelic surnames from 10th century. According to some sources, O Cleirigh is oldest recorded surname in Europe, first used by Tighernach Ua Cleirigh, Lord of Aidhne, who died 916 AD, making O'Clery oldest. So oldest Irish surname is O Cleirigh or O'Clery, dating to 10th century, with O'Conor also very old, making Irish surnames among oldest in Europe, predating English surnames, with Gaelic origin and meaning descendant of.