If an integer p is such that (8p+1) is prime, where p`gt`2, then (8p-1) is:

Options

A. divisible by 7
B. divisible by 3
C. a prime number
D. none of these

Answer

To solve the problem, we need to determine the value of \(8p - 1\) given that \(8p + 1\) is a prime number and \(p > 2\).

### Step-by-step Solution:

1. **Understanding the condition**: We know that \(8p + 1\) is a prime number. This means that for certain values of \(p\), \(8p + 1\) must not have any divisors other than 1 and itself.

2. **Testing values of \(p\)**: Since \(p\) must be greater than 2, we can start testing integer values of \(p\) starting from 3.

- For \(p = 3\):
\[ 8p + 1 = 8 \times 3 + 1 = 24 + 1 = 25 \quad (\text{not prime}) \]

- For \(p = 4\):
\[ 8p + 1 = 8 \times 4 + 1 = 32 + 1 = 33 \quad (\text{not prime}) \]

- For \(p = 5\):
\[ 8p + 1 = 8 \times 5 + 1 = 40 + 1 = 41 \quad (\text{prime}) \]

3. **Calculating \(8p - 1\)**: Now that we have found \(p = 5\) such that \(8p + 1\) is prime, we can calculate \(8p - 1\):
\[ 8p - 1 = 8 \times 5 - 1 = 40 - 1 = 39 \]

4. **Analyzing \(39\)**: We need to check the properties of \(39\):
- **Divisibility by 3**:
\[ 39 \div 3 = 13 \quad (\text{divisible by 3}) \]
- **Divisibility by 7**:
\[ 39 \div 7 \approx 5.57 \quad (\text{not divisible by 7}) \]
- **Prime check**: Since \(39\) can be divided by \(3\) (as shown above), it is not a prime number.

5. **Conclusion**: Since \(39\) is divisible by \(3\) and not a prime number, we conclude that \(8p - 1\) is divisible by \(3\).

### Final Answer:
The answer is that \(8p - 1\) is **divisible by 3**.