The first 100 prime numbers

The expression $4 \le n > 9$ is not a standard mathematical notation for a single compound inequality. However, the set $\{5, 6, 7, 8, 9\}$ is written below it. This set represents all integers $n$ such that $n$ is strictly greater than 4 and less than or equal to 9. This corresponds to the inequality $4 < n \le 9$.

For integers $n$ satisfying $4 < n \le 9$:

• $n$ must be greater than 4, so $n \in \{5, 6, 7, \dots\}$.
• $n$ must be less than or equal to 9, so $n \in \{\dots, 7, 8, 9\}$. Combining these conditions, the integers that satisfy both are $5, 6, 7, 8, 9$. The set you provided, $\boxed{\{5, 6, 7, 8, 9\}}$, is correct for the implied inequality $4 < n \le 9$.

A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself.

The first few prime numbers are:

Listing all 100 prime numbers is extensive. The 100th prime number is $\boxed{541}$.