The one that the Hebrews/Jews (Semites of today) still use today, is the Akkadian calendar. The Akkadians used a lunar calendar, and the names of each of the 12 months are exactly or nearly exactly the same as used today by the Jewish calendar. As Akkadian is the root language of Hebrew.
As an example;
Hebrew language Akkad language
What makes this year important, is this year also coincides to the same year that Naram-Sin proclaimed himself God and Master of the Universe, as the King of the Akkadian Semite people. This year of Naram-Sin can be verified by the cuneiform texts, now existing in the British Museum, of Nabonidus. The tablet states that a period of 3200 years elapsed between Nabonidus finding Naram-Sin's memorial temple foundation stone at Sippur, and the burial of that stone.
Further reading: Blog; The Akkadians
The following text is from the cylinder of Nabonidus; I removed the debris of that temple, looked for its old foundation deposit, dug to a depth of eighteen cubits into the ground and then Šamaš, the great lord, revealed to me the original foundations of Ebabbar, the temple which is his favorite dwelling, by disclosing the foundation deposit of Naram-Sin, son of Sargon, which no king among my predecessors had found in three thousand and two hundred years.
This would mean in 3760 B.C. at the height of Naram-Sin's reign, he decided to rebuild this important temple. This event then coincides with the beginning of the Jewish Semitic lunar calendar as year one. An interesting fact connecting modern Semitic people and those that lived and died centuries before.
Nabonidus began his reign what many suggest in the year 556 BC, and shortly afterward began his reclamation of ancient temples. By simply adding 555 years to 3200 years, the year 3755 BC is noted, which is very close to 3760 BC, and right in the middle of Naram-Sin's military conquests.
The Deification Ceremony of Naram-Sin could of have been combined as part of the completion of a temple, or the beginning of the temples construction. This is a very significant event/date that he would have choosen to celebrate as year one on the Akkadian Calendar, which all Semitic peoples down to this day recognize.
Many experts have disagreed with Nabonidus dating of Naram-Sin's account, stating that his records have to out by some 1500 years to correspond to their own dating of these accounts, The question is how could Nabonidus calculations be out by 1500 years, ( a very large number), when he was party to the study of Babylon's History? A study that he took very seriously using Babylon's ancient libraries, and as the text suggests, many of his predecessors did likewise. These libraries of ancient cuneiform writings that are not available for today's scholars to examine.
L.King's bell weather book; History of Summer and Akkad, published 100 years ago, discusses these very points.
The year that Naram-Sin, the first King to be defied, and his Semitic people proclaimed their King, was now named the Master of the Universe, is the same year that the Jewish Calendar appoints as year one. This is a clear indication of discovering the true Jewish history and their first god Dagan.
For further reading;