The given series is: \( 2, 3, 5, 7, 11, x, 17 \). Step 1: The series is a list of prime numbers. The missing number \( x \) is the next prime number after 11. Step 2: The prime numbers are: 2, 3, 5, 7, 11, 13, 17. Thus, the value of \( x \) is 13.