Chapter 11, Problem 68SGR

To determine

Find a counterexample for the statement $n^2+2n+4$ is prime.

Answer to Problem 68SGR

  $n=2$ is a counter example of the statement $n^2+2n+4$ is prime.

Explanation of Solution

Given:

  $n^2+2n+4$ is prime.

Concept Used:

Counterexample is an example which disproves a proposition.

For example, the prime number 2 is a counterexample to the statement "All prime numbers are odd."

Calculation:

  $n=2;n^2+2n+4=2^2+2·2+4=12\Rightarrow \text{Not}\text{a}\text{prime}$

  $n=2$ is a counter example.

Thus, $n=2$ is a counter example of the statement $n^2+2n+4$ is prime.