If the numbers `x, x+ 2 x + 4` are the primes, then x is equal to

Options

A. 3
B. 2
C. 11
D. 17

Answer

To solve the problem, we need to find the value of \( x \) such that the numbers \( x \), \( x + 2 \), and \( x + 4 \) are all prime numbers.

### Step-by-Step Solution:

1. **Understanding Prime Numbers**:
- A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The only divisors of a prime number are 1 and itself.

2. **Setting Up the Numbers**:
- We have three numbers: \( x \), \( x + 2 \), and \( x + 4 \). We need to check if all three numbers are prime.

3. **Testing Values for \( x \)**:
- We will test various values of \( x \) to see if all three numbers are prime.

4. **Testing \( x = 3 \)**:
- \( x = 3 \)
- \( x + 2 = 3 + 2 = 5 \)
- \( x + 4 = 3 + 4 = 7 \)
- All three numbers \( 3, 5, 7 \) are prime.

5. **Testing \( x = 2 \)**:
- \( x = 2 \)
- \( x + 2 = 2 + 2 = 4 \)
- \( x + 4 = 2 + 4 = 6 \)
- Here, \( 4 \) and \( 6 \) are not prime (they are composite).

6. **Testing \( x = 11 \)**:
- \( x = 11 \)
- \( x + 2 = 11 + 2 = 13 \)
- \( x + 4 = 11 + 4 = 15 \)
- Here, \( 15 \) is not prime (it is divisible by \( 3 \) and \( 5 \)).

7. **Testing \( x = 17 \)**:
- \( x = 17 \)
- \( x + 2 = 17 + 2 = 19 \)
- \( x + 4 = 17 + 4 = 21 \)
- Here, \( 21 \) is not prime (it is divisible by \( 3 \) and \( 7 \)).

8. **Conclusion**:
- The only value of \( x \) that makes all three numbers \( x, x + 2, x + 4 \) prime is \( x = 3 \).

### Final Answer:
Thus, the value of \( x \) is \( 3 \).

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