Which of the following is a finite set?

The primes strictly between $30$ and $70$ are $31, 37, 41, 43, 47, 53, 59, 61, 67$ — a definite, countable number of elements, so the set is finite. The other options ($\mathbb{N}$, $\mathbb{Z}$, $\mathbb{R}$) are all infinite.