According to evolutionary studies, prokaryotes may have arisen around

According to evolutionary studies, prokaryotes may have arisen around

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Explanation

The first fossils of prokaryotic (bacterial) cells are known from 3.5 and 3.4 billion years ago. 

while 

The eukaryotes developed at least 2.7 billion years ago, following some 1 to 1.5 billion years of prokaryotic evolution.