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?
[Math] Consecutive prime numbers
prime numbers
Best Answer
Yes, this is correct, due to Bertrand's Postulate :
Primes occur no further intervals than $n$ and $2n$, and $n^2>2n$ for $n>3$