Eight persons A, B, C, D, E, F, G, and H live on different floors of an eight-floor building, numbered 1 to 8 from bottom to top. One person lives on each floor but not necessarily in the given order.

G lives five floors above C. As many floors are there below C’s floor as above B’s floor. Three floors are there between the floors of B and D. F lives two floors away D. E does not live above H. A doesn’t live on prime numbered floor.

Which of the following statements is/are incorrect?
I. G lives on the topmost floor.
II. Two persons live between E and C.
III. B lives on a floor below H’s floor.

To determine which of the statements are incorrect, let us analyze the clues step-by-step to find the floor arrangement of the eight persons (A, B, C, D, E, F, G, and H) from floor 1 to floor 8.

Step 1: Determine the positions of G, C, and B
Clue 1: G lives five floors above C.
This means:
$\mathrm{Floor\; of\; G}-\mathrm{Floor\; of\; C}=\; 5$
The possible pairs for $(C,G)$ are:
Case A: $C=\; 1$, $G=\; 6$
Case B: $C=\; 2$, $G=\; 7$
Case C: $C=\; 3$, $G=\; 8$

Clue 2: As many floors are there below C’s floor as above B’s floor.
Number of floors below C is $C-\; 1$. Number of floors above B is $8-B$.
Therefore:
$C-\; 1\; =\; 8\; -B\Rightarrow C+B=\; 9$

Now, let's evaluate each case:
• Case A: If $C=\; 1$ and $G=\; 6$, then $B=\; 9\; -\; 1\; =\; 8$.
• Case B: If $C=\; 2$ and $G=\; 7$, then $B=\; 9\; -\; 2\; =\; 7$. However, this means both G and B would live on floor 7, which is a contradiction. Thus, Case B is eliminated.
• Case C: If $C=\; 3$ and $G=\; 8$, then $B=\; 9\; -\; 3\; =\; 6$.

Step 2: Placing D and F
Clue 3: Three floors are there between the floors of B and D.
• For Case A ($B=\; 8$): D must live on floor 4 (since floors 7, 6, and 5 are between them).
• For Case C ($B=\; 6$): D must live on floor 2 (since floors 5, 4, and 3 are between them).

Clue 4: F lives two floors away from D.
• For Case A ($D=\; 4$): F can live on floor 2 or floor 6. Since G is already on floor 6, F must be on floor 2.
• For Case C ($D=\; 2$): F must live on floor 4 (as floor 0 does not exist).

Step 3: Placing A, E, and H
Clue 5: A doesn't live on a prime numbered floor. The prime numbered floors in an 8-floor building are 2, 3, 5, and 7.
• For Case A:
Current positions: G on 6, C on 1, B on 8, D on 4, F on 2.
The vacant floors are 3, 5, and 7. All of these vacant floors are prime numbers. This leaves no non-prime floor available for A. Therefore, Case A is eliminated.
• For Case C:
Current positions: G on 8, C on 3, B on 6, D on 2, F on 4.
The vacant floors are 1, 5, and 7. Since 1 is not a prime number, A must live on floor 1.

Clue 6: E does not live above H (meaning E lives on a floor below H).
The remaining vacant floors are 5 and 7.
To satisfy $E<H$, E must live on floor 5 and H must live on floor 7.

Final Floor Arrangement:
Floor 8: G
Floor 7: H
Floor 6: B
Floor 5: E
Floor 4: F
Floor 3: C
Floor 2: D
Floor 1: A

Step 4: Evaluate the Statements
I. G lives on the topmost floor. (G lives on floor 8, which is the topmost floor. Correct)
II. Two persons live between E and C. (E lives on floor 5 and C lives on floor 3. Only one person, F on floor 4, lives between them. Incorrect)
III. B lives on a floor below H’s floor. (B lives on floor 6 and H lives on floor 7. Since 6 is below 7, this is Correct)

Therefore, only statement II is incorrect.