(Solved): Find the flaw in this induction proof. Let P(n) be the statement that n2+n+11 is prime where n1 ...

Find the flaw in this induction proof. Let $P(n)$ be the statement that $n^2+n+11$ is prime where $n\ge 1$ is an integer. Step 1: $P(1)$ is true because $1^2+1+11=13$ is prime. Step 2: Assume $P(k)$ is true for some integer $k\ge 1$, that is, $k^2+k+11$ is prime for some integer $k\ge 1$. $\begin{array}{l}\text{ Step 3: By algebra, }(k+1{)}^2+(k+1)+11=\\ =\left(k^2+2k+1\right)+(k+1)+11=\\ =\left(k^2+k+11\right)+2k+2.\end{array}$ Step 4: By the inductive hypothesis, $k^2+k+11$ is prime. Step 5: Therefore $\left(k^2+k+11\right)+2k+2$ is also prime. Step 6: So $(k+1{)}^2+(k+1)+11$ is prime and $P(k+1)$ is true. The flaw is in Step