When did sumerian exist ?
I assume you mean when did the Sumerian civilisation exist. Sumer (Shumer, Sumeria, Shinar, native ki-en-gir) formed the southern part of Mesopotamia from the time of settlement by the Sumerians around 4000 BCE, until the time of Babylonia around 2000 BCE. Its location was in the southern part of the Tigris-Euphrates plain. The cities of Sumer were the first civilisation to practice intensive, year-round agriculture. The surplus of storable food created by this economy allowed the population to settle in one place instead of migrating after crops and grazing land. It also allowed for a much greater population density and in turn required an extensive labor force and division of labor. Sumer was also the site of early development of writing, progressing from a stage of proto-writing in the mid 4th millennium BCE to writing proper by 3000 BCE.