First, we know that $ x $ is even. Every prime number larger than $ 3 $ is odd, so the sum of three members has to be even. Now, $ 12 $ does not work because $ (2+10+12)+1=25 $, which is not prime. Similarly, $ 14 $ does not work because $ (2+4+14)+1=21 $, which is not prime. But $ 16 $ works because all the possible sums involving $ x=16 $ generate prime results: $ (2+4+16)+1=23 $, $ (2+10+16)+1=29 $, and $ (4+10+16)+1=31 $. So the smallest possible value of $ x $ is $ \boxed{16} $.