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Number theory Difficulty 1.0 Junior Find the answer United Kingdom

Which of the following values of $n$ is a counterexample to the statement, 'If $n$ is a prime number, then exactly one of $n-2$ and $n+2$ is prime'?

(A) $11$ (B) $19$ (C) $21$ (D) $29$ (E) $37$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.