Bertand's Postulate

[a1call]

This proof can be modified to prove that for any positive integer k, there is a number N such that for all n > N, there are k primes between n and 2n.

https://primes.utm.edu/glossary/page...randsPostulate

That does not sound right to me. Shouldn't that be something like:

This proof can be modified to prove that for any positive integer k, there is a number N such that for all n > N, there are at least k primes between n and 2n.

Thank you for your time.

[a1call]

Follow up question:
* Is there a (known) way to formulate N as a function of k?

Thanks in advance.

[R. Gerbicz]

Originally Posted by a1call

https://primes.utm.edu/glossary/page...randsPostulate
That does not sound right to me. Shouldn't that be something like:

That is correct wording.
You can say stronger statement (following and modifying the proof) : there is c0>0 for that there is at least c0*n/log(n) primes in [n,2n]. Using this there is c1>0 for that for N=c1*n*log(n) there is at least n primes in [N,2N].

[a1call]

Thank you very much for the confirmation and the formulation R. Gerbicz.