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Let $x$ be a positive integer and $y = x^2+2$. Can $x$ and $y$ be both prime? The answer is yes,  since for $x=3$ we get $y=11$, and both numbers are prime. Prove that this is the only value of  $x$ for which both $x$ and $y$ are prime.  ANSWER: If $x$=$ (mod $),then for $x$ to be prime $x$ must be $. If $x$=$(mon$), then $x$ has to be $.The this shows that the next $x$ will be prime relative to $3$.We can then assume $x$=$m+$, and $y$=n$+$ , since odd numbers can be represented as $2$n+$1$ and $2$m$+$1$ where mand n are integers.}