<s>[INST] If $x$, $y$, $x+y$, and $x-y$ are prime numbers, what is their sum? 
Suppose that $x$, $y$, $x−y$, and $x+y$ are all positive prime numbers. What is the sum of the four numbers?

Well, I just guessed some values and I got the answer.
$x=5$, $y=2$, $x-y=3$, $x+y=7$. All the numbers are prime and the answer is $17$.
Suppose if the numbers were very big, I wouldn't have got the answer.
Do you know any ways to find the answer?
 [/INST] If $x,y > 1$ are both odd, then $x+y > 2$ is even, a contradiction.
Then $y = 2$ and by inspection $x=5$ as $x = 3$ results in $x-y = 1$.
Or, we have that $x-2,x,x+2$ are all prime meaning we have three consecutive integers modulo $3$ which is only satisfied by the triple $(3,5,7) \implies y = 5$.
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