Let $n$, $m$ are two positive integer numbers for $n \ge 2$, $m \ge 1$; $P_n$ is $n$-$th$ prime number. How I can prove that:
Let $n > 1$ and $m > 0$ be two integers and $P_n$ be the $n^{th}$ prime.
$$P_{n+m} \ge P_n+P_m$$ Prove: $$P_{n+m} \ge P_n + P_m .$$
Can you give for me a hint, a reference, or a comment, or a proof?
Can you give a hint, reference, comment, or proof?
