Elementary Methods in Number Theory Exercise 1.5.2

Let $N=210$.Prove that $N-p$ is prime for every prime $p$ such that $\frac{N}{2}<p<N$.Find a prime number $q<\frac{N}{2}$ such that $N-q$ is composite.

 

Proof:
\begin{align*}
210-199 =11\\
210-197 =13\\
210-193=17\\
210-191=19\\
210-181=29\\
210-179=31\\
210-173=37\\
210-167=43\\
210-163=47\\
210-157=53\\
210-151=59\\
210-149=61\\
210-139=71\\
210-137=73\\
210-131=79\\
210-127=83\\
210-113=97\\
\end{align*}
This is fairly strange.
\begin{equation}
210-41=169=13^{2}
\end{equation}