Let $P (n)$ be the statement that $n^{2} - n + 41$ is prime, then which of the following is not true ?

P (2)

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P (3)

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P (41)

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none of these

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Solution

The correct option is C $P (41)$
given that $P (n) = n^{2} - n + 41$
$P (2) = 2^{2} - 2 + 41 = 43$ (prime true)
$P (3) = 3^{2} - 3 + 41 = 47$ (prime true)
$P (41) = 41^{2} - 41 + 41 = {(41)}^{2}$
$∴ P (41)$ is not true
Ans: C

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