For $n\ge6$, there are at least two primes in the interval between $n$ and $2n$. Does anyone know of an already established and accepted proof for this? A reference would be helpful.
I have read in an answer to this question - Primes between $n$ and $2n$ - that for $n\ge25$, there are at least three primes between $n$ and $2n$.
Simply checking the gaps for all $n$ up to 25 would complete the proof.
I came up with my own proof to prove something else. So I want a different proof from my own.
So my question is, is it safe to base a proof for something else on this fact?:
For $n\ge6$, there are at least two primes in the interval between $n$ and $2n$.
Where can I find a reference?
Ramanujan's proof of Bertrand's postulate gives this result (and more). Reference:
S. Ramanujan, A proof of Bertrand's postulate, Journal of the Indian Mathematical Society 11 (1919), pp. 181–182.