:I can't quite figure it out. The system of numbering dynasties was developed by Manetho in the Thirtieth Dynasty, so it isn't often applied to later dynasties. But it looks like the second period of Achamenid rule, following the Thirtieth Dynasty, is sometimes called the Thirty-first Dynasty. One might count the Ptolemies as the Thirty-second Dynasty, but I don't know if any reliable sources do so. They're either called "the Ptolemaic dynasty" or "the Ptolemies" or "the Lagides". And counting them as number 32 instead of 33 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 can't see any reason for counting the Ptolemies as number 34. Unless sources address the issue, I think attempts to give the Ptolemies a number should be left out of the article.