1) Determine what is wrong with the following proof. 2) Determine if the stateme

ID: 3145232 • Letter: 1

Question

1) Determine what is wrong with the following proof.

2) Determine if the statement of the theorem is true or false

3) If it is true, give a correct proof.

4) If it is false, prove that its is false.

“Theorem”. If n is a natural number then n 2 + n + 41 is a prime number.

Here is the proof:

• For n = 1, n^2 + n + 41 = 43, and 43 is prime.

• For n = 2, n^2 + n + 41 = 47, and 47 is prime.

• For n = 3, n^2 + n + 41 = 53, and 53 is prime.

• For n = 4, n^2 + n + 41 = 61, and 61 is prime.

• For n = 5, n^2 + n + 41 = 71, and 71 is prime.

• For n = 6, n^2 + n + 41 = 83, and 83 is prime.

• For n = 7, n^2 + n + 41 = 97, and 97 is prime.

• · · ·

• Similarly, for n = 8, 9, 10 and so on, n 2 + n + 41 is prime.

So (n IN)n 2 + n + 41 is prime . Q.E.D

for n=40 n^2+n+41=40^2+40+41=1681=41*41 which is not a prime number

if n is a natural number then n 2 + n + 41 is a prime number for n<40

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