If `P(n)` is the statement `n^2-n+41` is prime. Prove that `P(1),\ P(2)` and `P(3)` are true. Prove also that `P(41)` is not true.

Explanation

`x^2−x+41`

`P(n)=x^2−x+41` is a prime number

`P(1)=1^2−1+41` is a prime No. of
`P(1)=41` is prime, which is true

`P(2)=2^2−2+41` is a prime No, i.e.,
`P(2)=43` is prime No, which is true

`P(211)=(41)^2−41+41` is a prime No,
i.e.,` P(41)=(41)^2 `is a primes which is Not true.