New Byzantine calendar

The New Byzantine Calendar was a calendar used by multiple races, including some humans and Hath. Dates were written as a four-digit year, a two-digit month and a two-digit day. For example, 24 July 6012 would be written as "60120724". (DW: The Doctor's Daughter) In said episode, Donna suggested that the first two digits could be some sort of "big old space date", with the two-digit year, month, and day following it. It is unclear which system was used.

Behind the scenes
It is unclear exactly when the New Byzantine Calender was in use - whether it was just a different version of writing dates (so, the 61st century) or an entirely new dating system. A New Roman Empire was mentioned to exist in the year 12005 in The End of the World, but other than the name (the Byzantine Empire was the name given to the Eastern Roman Empire in the real world) there is little to connect them. Another possible origin might be the city of New Byzantium mentioned in Shadowmind. This could suggest there was a "New Byzantine Empire", that had succeeded the New Roman Empire.