I have always wanted to ask this. I could never understand why The Roman Church was seen as first with Constantinpole as second and Alexandria as third and Antioch as Fourth and Jerusalem as fifth. I know that Peter died in Rome as well as Paul. what I don't understand is the Church started in Jerusalem. Jerusealem was the seat of King David and that Jesus was born in the Family line of king David and so the church started in Jerusalem Israel. it should have been the First in line stead of Rome.
By the time of "ranking" of the patriarchates, Jerusalem had long since become a fairly meaningless town. It was destroyed pretty well in AD 70. Rome and Constantinople, being the two major cities of Christendom, understandably had pride of place.