The set of integers $\{2,4,10,x\}$ has the property that the sum of any three members of the set plus 1 yields a prime number. What is the smallest possible value of $x$ greater than 10?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
The set of integers $\{2,4,10,x\}$ has the property that the sum of any three members of the set plus 1 yields a prime number. What is the smallest possible value of $x$ greater than 10?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
16
The set of integers $\{2,4,10,x\}$ has the property that the sum of any three members of the set plus 1 yields a prime number. What is the smallest possible value of $x$ greater than 10?
train