Consider the following statements
A.The sum of two prime numbers is a prime number.
B. The product of two prime numbers is a prime number.
Which of these statements is/are correct?

Options

A. Neither A nor B
B. A alone
C. B alone
D. Both A and B

Answer

To determine the correctness of the statements A and B, we will analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** The sum of two prime numbers is a prime number.

1. **Choose two prime numbers:** Let's take 2 and 7.
2. **Calculate their sum:**
\[ 2 + 7 = 9 \]
3. **Check if the result is a prime number:**
- A prime number is defined as a number greater than 1 that has no positive divisors other than 1 and itself.
- The number 9 has divisors 1, 3, and 9, which means it is not a prime number.

**Conclusion for Statement A:** The sum of 2 and 7 is 9, which is not a prime number. Therefore, Statement A is incorrect.

### Step 2: Analyze Statement B
**Statement B:** The product of two prime numbers is a prime number.

1. **Choose two prime numbers:** Let's take 2 and 3.
2. **Calculate their product:**
\[ 2 \times 3 = 6 \]
3. **Check if the result is a prime number:**
- The number 6 has divisors 1, 2, 3, and 6, which means it is not a prime number.

**Conclusion for Statement B:** The product of 2 and 3 is 6, which is not a prime number. Therefore, Statement B is also incorrect.

### Final Conclusion
Both statements A and B are incorrect. Thus, the answer is that neither statement is correct.

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