Which one is correct in the following statements?

Options

A. A composite number may be odd number.
B. Least prime number is 1.
C. Sum of two prime numbers always prime number.
D. Even prime number does not exist.

Explanation

To solve the question, we need to evaluate the correctness of the given statements about composite and prime numbers. Let's analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** A composite number may be an odd number.

- **Definition of Composite Numbers:** A composite number is a positive integer that has at least one positive divisor other than one or itself. This means it can be divided evenly by numbers other than 1 and itself.
- **Example:** The number 9 is a composite number because it can be divided by 1, 3, and 9. It is also an odd number.

**Conclusion for Statement 1:** This statement is correct because composite numbers can indeed be odd.

### Step 2: Analyze Statement 2
**Statement 2:** The least prime number is 1.

- **Definition of Prime Numbers:** A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. In other words, it has exactly two distinct positive divisors: 1 and itself.
- **Correct Information:** The least prime number is actually 2, not 1.

**Conclusion for Statement 2:** This statement is incorrect.

### Step 3: Analyze Statement 3
**Statement 3:** The sum of two prime numbers is always a prime number.

- **Counterexample:** Let's take two prime numbers, 5 and 7. Their sum is 12, which is not a prime number (as it has divisors other than 1 and itself).

**Conclusion for Statement 3:** This statement is incorrect.

### Step 4: Analyze Statement 4
**Statement 4:** Even prime number does not exist.

- **Correct Information:** The number 2 is the only even prime number because it is divisible by 1 and 2 only.

**Conclusion for Statement 4:** This statement is incorrect.

### Final Conclusion
After analyzing all statements, we find that:

- **Statement 1 is correct.**
- **Statements 2, 3, and 4 are incorrect.**

Thus, the correct answer is that the first statement is the only correct one.