If $x$ is a prime such that $(x^2+3)$ is also a prime, then $x$ can have
A2 values
B1 value
Cmore than 2 values
DNone of these
Answer & Solution
Correct answer: B. 1 value
The key idea is parity. If $x=2$, then $x^2+3=4+3=7$, which is prime. For any other prime $x$, $x$ is odd, so $x^2$ is odd and $x^2+3$ is even; since it is greater than 2, that even number cannot be prime. Therefore only $x=2$ works, so $x$ has exactly one value.
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