Which one of the following statements is correct?

Options

A. sum of two prime numbers is always a prime number
B. 1 is the smallest prime number
C. a composite number can be odd
D. there is no even prime number

Answer

To determine which statement is correct, let's analyze each statement one by one.

1. **Sum of two prime numbers is always a prime number.**
- A prime number is defined as a positive integer greater than 1 that has exactly two distinct positive divisors: 1 and itself.
- Let's consider the sum of two prime numbers. For example, if we take 2 (the only even prime number) and another prime number like 3, their sum is 5, which is prime. However, if we take two odd prime numbers, such as 3 and 5, their sum is 8, which is not prime. Therefore, this statement is incorrect.

2. **One is the smallest prime number.**
- By definition, the smallest prime number is 2. The number 1 is not considered a prime number because it does not meet the requirement of having exactly two distinct positive divisors. Hence, this statement is also incorrect.

3. **A composite number can be odd.**
- A composite number is defined as a positive integer that has at least one positive divisor other than one or itself, meaning it has more than two factors. An example of an odd composite number is 9 (which has factors 1, 3, and 9). Therefore, this statement is correct.

4. **There is no even prime number.**
- This statement is incorrect because 2 is an even number and is also a prime number.

Based on the analysis, the correct statement is:
**A composite number can be odd.**

### Steps Summary:
1. Analyze the first statement about the sum of two prime numbers.
2. Check the definition of prime numbers and verify the second statement about 1.
3. Define composite numbers and verify the third statement about odd composite numbers.
4. Evaluate the fourth statement regarding even prime numbers.