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Topic: Gaps between primes
Replies: 6   Last Post: Oct 17, 2013 10:00 AM

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Luis A. Rodriguez

Posts: 731
Registered: 12/13/04
Re: Gaps between primes
Posted: Oct 17, 2013 10:00 AM
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El miércoles, 16 de octubre de 2013 11:01:48 UTC-4:30, Ludovicus escribió:
> Have someone demonstrated that gap p(n+1) - p(n) < sqr[p(n)] for p(n) >113 ?
>
> If not, I will show proximately, that theorem.
>
> Ludovicus


Dear friends.
I beg your pardon. I commited a serious error.
I was manipulating Dusart inequalities: x /(log(x) - 1) < Pi(x) ; X > 5392
and Pi(x) < x / (log(x) - 1.1) ; x > 60435
Then, by an algebraic error I arrived at that false conclusion.
If the difference of those inequalities could be < sqr(p(n)) then the Riemman
Hypothesis would follow.
The proposition is true only for p(n) < 5 x 10^6



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