Consecutive prime numbers

Question

Let's assume $k$ and $n$ are consecutive prime numbers, $k \lt n$.

An axiom: for any such $k$ and $n$, $k^2 \gt n$.

This seems "obviously" true to me, but could you please prove me wrong? Or if it is correct, could you please help me prove it?

Answer 1

Yes, this is correct, due to Bertrand's Postulate :

Primes occur no further intervals than $n$ and $2n$, and $n^2>2n$ for $n>3$