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, we can construct the step-by-step floor arrangement for the eight persons A, B, C, D, E, F, G, and H on the 8-floor building (numbered 1 to 8 from bottom to top).

Let us list the clues and build the arrangement:
1. G lives five floors above C: This means the floor of G minus the floor of C is equal to 5 (Floor_G - Floor_C = 5). The possible pairs for (C, G) are:
- If C is on floor 1, G is on floor 6.
- If C is on floor 2, G is on floor 7.
- If C is on floor 3, G is on floor 8.

2. As many floors are there below C’s floor as above B’s floor: This means if C is on floor $x$ (with $x-1$ floors below it), then B must be on floor $9-x$ (so that there are $9-x-1=8-x$ floors above it, which matches $x-1$). Let's test the three cases:
- Case 1: C is on floor 1, G is on floor 6. Since C is on floor 1, B must be on floor 8.
- Case 2: C is on floor 2, G is on floor 7. Since C is on floor 2, B must be on floor 7. But G is already on floor 7, so this case is invalid.
- Case 3: C is on floor 3, G is on floor 8. Since C is on floor 3, B must be on floor 6.

Let's analyze the remaining conditions for the two viable cases:

Case 1: C = 1, G = 6, B = 8
- Three floors are there between B and D: Since B is on floor 8, there are three floors between them (7, 6, 5), which puts D on floor 4.
- F lives two floors away from D: This means F can be on floor 2 or floor 6. Since G is already on floor 6, F must be on floor 2.
- At this stage, the occupied floors are: 8 (B), 6 (G), 4 (D), 2 (F), 1 (C).
- The remaining floors are 3, 5, and 7. The remaining persons are A, E, and H.
- A doesn’t live on a prime numbered floor: The remaining floors are 3 (prime), 5 (prime), and 7 (prime). Since all remaining floors are prime numbers, A would have to live on a prime numbered floor, which violates the condition. Thus, Case 1 is invalid.

Case 3: C = 3, G = 8, B = 6
- Three floors are there between B and D: Since B is on floor 6, the three floors between them are 5, 4, 3, which puts D on floor 2.
- F lives two floors away from D: This means F is either on floor 4 or floor 0 (not possible). So F must be on floor 4.
- At this stage, the occupied floors are: 8 (G), 6 (B), 4 (F), 3 (C), 2 (D).
- The remaining floors are 7, 5, and 1. The remaining persons are A, E, and H.
- A doesn’t live on a prime numbered floor: The remaining floors are 7 (prime), 5 (prime), and 1 (not prime). Therefore, A must live on floor 1.
- The remaining floors for E and H are 7 and 5.
- E does not live above H: This means E must live on a floor below H. Thus, E must live on floor 5 and H must live on floor 7.

The final floor arrangement from top to bottom (floors 8 to 1) is:
Floor 8: G
Floor 7: H
Floor 6: B
Floor 5: E
Floor 4: F
Floor 3: C
Floor 2: D
Floor 1: A

Now, let's check the statements:
- I. G lives on the topmost floor: True, G lives on floor 8.
- II. Two persons live between E and C: False, E is on floor 5 and C is on floor 3. Only one person (F, on floor 4) lives between E and C.
- III. B lives on a floor below H’s floor: True, B is on floor 6, which is below H's floor (floor 7).

Since only statement II is incorrect, the correct option is "Only II".