I cant quite figure it out The system of numbering dynasties was developed by Manetho in the Thirtieth Dynasty so it isnt often applied to later dynasties But it looks like the second period of Achamenid rule following the Thirtieth Dynasty is sometimes called the Thirtyfirst Dynasty One might count the Ptolemies as the Thirtysecond Dynasty but I dont know if any reliable sources do so Theyre either called the Ptolemaic dynasty or the Ptolemies or the Lagides And counting them as number  instead of  would ignore the Argead Dynasty Alexander the Great his son Alexander IV of Macedon and Philip III Arrhidaeus which ruled briefly but probably as long as some of the minor numbered dynasties I cant see any reason for counting the Ptolemies as number  Unless sources address the issue I think attempts to give the Ptolemies a number should be left out of the article