**Notation:** For any $n\geq 1$ let $p_{n}$ be $n$-th prime number.

**Definition:** A prime number $p_{n}$ is "additive" iff $p_{n}=\sum_{i<n} p_{i}$

**Example:** $5$ is an additive prime number.

**Question (1):** What is the least additive prime number larger than $5$?

**Question (2):** Are there infinitely many additive prime numbers?

**Question (3):** If $p_{n}$ be an additive prime number, is $n$ a prime number too?