Let $p_n$ represent the $n$th prime number. Is the following formula necessarily true?
$$p_n^2 > p_{n+1}$$
Experimentally, it seems true but I don't know enough number theory to prove it. My problem is that I don't know enough number theory to relate primes to each other. I know enough math to use the prime number theorem to prove it for sufficiently large $n$ but I can't prove it in general.
My question is whether this relationship is true in general and, if so, what is a proof for this result?
Thank you...