What's special about the set $C=\{23,29, 31, 37\}$ that its sum of the reciprocals is equal to the four times the reciprocal average of $C$ squared?

Question

$S$ is the sum of the reciprocals of the squares of the prime numbers between $19$ and $41$,exclusive. Which of the following is closest to the value of $S$?

The trick is to notice that $C=\{23,29, 31, 37\}$ are on average $30$, so then we can do $4 \cdot (\dfrac{1}{30^2}).$

I think this is way too handy-wavy.

When is the sum of sqared reciprocals equal to the reciprocal of the sum squared I think is unrelated.