Justinian's law speaks of five patriarchates — Rome, Constantinople, Alexandria, Antioch, Jerusalem — in that order, and the arrangement is called the pentarchy. It was never quite the fact it was legislated as: Jerusalem was small, Constantinople was new, and by the time the theory was tidy the Arab conquest had put three of the five under a caliphate. It survives as the shape of the argument rather than as a working government, and every later dispute about primacy is conducted in its vocabulary.
The Early Church · ch. 15