If \( \mathrm{P}(n) \) is the statement " \( n^{2}-n+41 \) is prime...

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If \( \mathrm{P}(n) \) is the statement " \( n^{2}-n+41 \) is prime", show that \( \mathrm{P}(1), \mathrm{P}(2) \), and \( \mathrm{P}(3) \) are true but \( \mathrm{P}(41) \) is not true.
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