Rimush was the second king of the Akkadian Empire. He was the son of Sargon of Akkad

Sargon of Akkad

Sargon of Akkad, also known as Sargon the Great "the Great King" , was an Akkadian emperor famous for his conquest of the Sumerian city-states in the 23rd and 22nd centuries BC. The founder of the Dynasty of Akkad, Sargon reigned in the last quarter of the third millennium BC...

 and Queen Tashlultum

Tashlultum

Tashlultum was a queen of Akkad and wife of King Sargon of Akkad. She was the mother of his children Enheduanna, Rimush, Manishtushu, Shu-Enlil and Ilaba'is-takal. She was a grandmother of Naram-Sin of Akkad and great-grandmother of Shar-Kali-Sharri....

. He was succeeded by his brother Manishtushu

Manishtushu

Manishtushu was a king of the Akkadian Empire from 2276 to 2261 BC. His name is also spelled as Maništušu.- Biography :Manishtushu was the son of Sargon of Akkad and Queen Tashlultum, brother of En-hedu-ana and the father of Naram-Sin...

 and was an uncle of Naram-Sin of Akkad.
According to the Sumerian king list

Sumerian king list

The Sumerian King List is an ancient manuscript originally recorded in the Sumerian language, listing kings of Sumer from Sumerian and neighboring dynasties, their supposed reign lengths, and the locations of "official" kingship...

, his reign lasted 9 years (though variant copies read 7 or 15 years.) There is one surviving year-name for an unknown year in his reign: "Year in which Adab

Adab

Adab or Udab was an ancient Sumerian city between Telloh and Nippur. It was located at the site of modern Bismaya or Bismya in the Wasit Governorate of Iraq.-History:...

was destroyed".