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Old 2019-08-21, 23:22   #1
a1call
 
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"Rashid Naimi"
Oct 2015
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Default 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.
Thank you for your time.
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Old 2019-08-21, 23:30   #2
a1call
 
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"Rashid Naimi"
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Follow up question:
* Is there a (known) way to formulate N as a function of k?

Thanks in advance.
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Old 2019-08-22, 08:24   #3
R. Gerbicz
 
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"Robert Gerbicz"
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Quote:
Originally Posted by a1call View Post
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].
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Old 2019-08-24, 01:21   #4
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Thank you very much for the confirmation and the formulation R. Gerbicz.
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