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2019-08-21, 23:22   #1
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

3·641 Posts
Bertand's Postulate

Quote:
 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:

Quote:
 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.

 2019-08-21, 23:30 #2 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 3·641 Posts Follow up question: * Is there a (known) way to formulate N as a function of k? Thanks in advance.
2019-08-22, 08:24   #3
R. Gerbicz

"Robert Gerbicz"
Oct 2005
Hungary

141010 Posts

Quote:
 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].

 2019-08-24, 01:21 #4 a1call     "Rashid Naimi" Oct 2015 Remote to Here/There 78316 Posts Thank you very much for the confirmation and the formulation R. Gerbicz.

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