To solve this problem, we need to identify the primitive prokaryotes responsible for the production of biogas from the dung of ruminant animals.$\newline$Let's analyze each option:$\newline \bullet$Halophiles:$\newline$ - Halophiles are microorganisms that thrive in high salt concentrations.$\newline$ - They are not involved in biogas production.$\newline \bullet$Thermoacidophiles:$\newline$ - Thermoacidophiles are microorganisms that thrive in hot and acidic environments.$\newline$ - They are not involved in biogas production.$\newline \bullet$Methanogens:$\newline$ - Methanogens are a group of archaea that produce methane as a metabolic byproduct.$\newline$ - They are commonly found in the digestive tracts of ruminants and are responsible for the production of biogas.$\newline$ - Therefore, methanogens are the correct answer.$\newline \bullet$Eubacteria:$\newline$ - Eubacteria, or true bacteria, are a large group of bacteria but are not specifically responsible for biogas production.$\newline$Now, let's identify the correct option:$\newline$The primitive prokaryotes responsible for the production of biogas from the dung of ruminant animals are methanogens.$\newline$This corresponds to Option 3.