Limmu in the context of "Ishme-Dagan I"

Erishum I or Erišu(m) I (inscribed e-ri-šu, or APIN-ìš in later texts but always with an initial i in his own seal, inscriptions, and those of his immediate successors, “he has desired,”) c. 1974–1935 BCE (middle chronology), son of Ilu-shuma, was the thirty-third ruler of Assyria to appear on the Assyrian King List. He reigned for forty years. One of two copies of the Assyrian King List which include him gives his reign length as only 30 years, but this contrasts with a complete list of his limmu, some 40, which are extant from tablets recovered at Karum Kanesh. He had titled himself both as, "Ashur is king, Erishum is vice-regent" and the, “Išši’ak Aššur” (“steward of Assur”), at a time when Assur was controlled by an oligarchy of the patriarchs of the prominent families and subject to the “judgment of the city”, or dīn alim. According to Veenhof, Erishum I’s reign marks the period when the institution of the annually appointed limmu (eponym) was introduced. The Assyrian King List observes of his immediate predecessors, “in all six kings known from bricks, whose limmu have not been marked/found”.

Ilu-shuma or Ilu-šūma, inscribed DINGIR-šum-ma, (died c. 1974 BC) was a king of Assyria in the early 20th century BC. The length of his reign is uncertain, as the Assyrian King List records him as one of the "six kings whose names were written on bricks, but whose eponyms are not known", referring to the lists of officials after which years were named.

His son, Erishum I, is identified as the king who succeeded him and reigned for 40 years (or 30, depending on the copy of the Assyrian King List), followed by Erishum I's son, Ikunum. He titled himself "vice-regent of Assur, beloved of the god Ashur and the goddess Ishtar." The Synchronistic King List records, "eighty-two kings of Assyria from Erishum I, son of Ilu-shuma, to Ashurbanipal, son of Esarhaddon", in the concluding colophon.

In the history of Assyria, the eponym dating system was a calendar system for Assyria, for a period of over one thousand years. Every year was associated with the name, an eponym, of the Limmu, the official who led that year's New Year festival.

The dating system is thought to have originated in the ancient city of Assur, and remained the official dating system in Assyria until the end of the Assyrian Empire in the seventh century BC. The names of the limmu who became eponyms were originally chosen by lot sortition, until the first millennium it became a fixed rotation of officers headed by the king who constituted the limmu. The earliest known attestations of a year eponyms are at Karum-Kanesh, and became used in other Assyrian colonies in Anatolia. Its spread was due to Shamshi-Adad I's unification of northern Mesopotamia.