* Bacteria and blue-green algae (cyanobacteria) are both prokaryotes: This is absolutely true. They lack a nucleus and other membrane-bound organelles, which is a defining characteristic of prokaryotes.
* They are both primitive: While both are ancient life forms, "primitive" can be misleading. They have evolved and diversified significantly over billions of years. It's more accurate to say they are simple in structure compared to eukaryotes, but their functions and roles in ecosystems are complex.
* They live on Earth: Yes, they are ubiquitous on Earth, in diverse environments from soil and water to the human body.
Therefore, the statement is correct in its essence, but "primitive" should be replaced with "simple" or "ancient" for greater accuracy.
