How much time passed between the appearance of the first prokaryotic cells and the emergence of multicellular organisms?

Prokaryotes were the first organisms to evolve on Earth, so, the first prokaryotic cells appeared 3.8 billion years ago. After them, Eukaryotic unicellular organisms developed, when one cell engulfed the other cell (endosymbiotic theory). Those unicellular eukaryotes form multicellular aggregates and that represents an evolutionary transition from single cells to multicellular organisms. Multicellular organisms evolved from unicellular eukaryotes at least 1.7 billion years ago.

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