Consider the statement: `"P(n): n^(2)-n+41` is prime". Then which one of the following is true?

Options

A. Both P(3) and P(5) are false
B. P(3) is false but P(5) is true
C. Both P(3) and P(5) are true
D. P(5) is false but P(3) is true

Answer

C

Explanation

`P(n)=n^(2)-n+41`
`P(3)=47`
`P(5)=61`
Both are prime.
In fact the first composite number in the set of naturals is `P(41)=(41)^(2)`,