Step 1: Recall the divide.
Prokaryotes lack a true nucleus and membrane-bound organelles, while eukaryotes have both.
Step 2: List prokaryote features.
No true nucleus, no membrane-bound organelles, and usually circular DNA.
Step 3: Test bacteria and blue green algae.
Bacteria are classic prokaryotes, and blue green algae are cyanobacteria, also prokaryotic.
Step 4: Test mycoplasma.
Mycoplasma are the smallest cells and lack a cell wall, but they are still prokaryotes.
Step 5: Test fungi.
Fungi have a true nucleus and membrane-bound organelles, so they are eukaryotes.
Step 6: Conclude.
The one that is not a prokaryote is fungi, which is option 1.
\[ \boxed{\text{Fungi}} \]