[seqfan] Re: Is there any problems with this proof?

[John W. Nicholson]

Alexei Kourbatov,
First of all thanks for being clear with your concerns. Second, do remember the note:

"All gaps g_i = p_{i+1} − p_i, where p_i < p_y are g_i <= G_n(x)."

Maybe I need to add the following:

Under the assumption that the smaller gap is p_{y-b+1} - p_{y-b} = G_n(x), we see that the larger gap is p_{y+1} - p_y <= 2*G_n(x).

Is that OK? John W. Nicholson 

     On Sunday, February 22, 2015 5:17 PM, Alexei Kourbatov <akourbatov at gmail.com> wrote:
   
 

 In Cramer's model, I feel that both statements are true with probability 1.

In the original proof, the last sentence "So the gap g_y ..." apparently
does not follow from the preceding statements (as far as I can tell).
To illustrate my point: a-c < 2(b-d) does not follow from { a < 2b and c <
2d} - but it would follow e.g. from { a < 2b and c >= 2d}



On Sat, Feb 21, 2015 at 7:42 AM, Charles Greathouse <
charles.greathouse at case.edu> wrote:

> I don't know what to think of the first question. It's numerically
> unassailable -- to build up evidence in the primes, one way or another,
> you'd probably need to get a lot closer to a googolplex than a googol, and
> even 10^20 is out of reach at the moment. The only recourse I see is
> checking whether it holds in the Cramer model, flawed as it is.
>
> It wouldn't surprise me at all if ratios > 2 occurred infinitely often. It
> also wouldn't surprise me if it happened only finitely often.
>
> Charles Greathouse
> Analyst/Programmer
> Case Western Reserve University
>
> On Fri, Feb 20, 2015 at 7:58 PM, John W. Nicholson <reddwarf2956 at yahoo.com
> >
> wrote:
>
> > Charles,
> >
> > Does that mean that the proof with first question, that the ratio <=2, is
> > correct and with out problems so that you are now looking at the second
> > question with the limit of the ratio going to infinity =1? John W.
> Nicholson
> >
> >      On Friday, February 20, 2015 4:24 PM, Charles Greathouse <
> > charles.greathouse at case.edu> wrote:
> >
> >
> >
> >  I suspect that there is some k > 1 such that the ratio is greater than k
> > infinitely often. Is anyone interested in crunching the numbers here on
> the
> > heuristic?
> >
> > Charles Greathouse
> > Analyst/Programmer
> > Case Western Reserve University
> >
> > On Fri, Feb 20, 2015 at 4:53 AM, John W. Nicholson <
> reddwarf2956 at yahoo.com
> > >
> > wrote:
> >
> > > Below is a proof based on A005250(n ) of the OEIS.  Can someone look at
> > it
> > > and tell me if it true?
> > >
> > >
> >
> http://math.stackexchange.com/questions/1155523/is-frac-textnext-maximal-textmaximal-2-true
> > > If it is true, an edit of A005250 comments is needed.
> > >
> > > Related:
> > >
> > >
> >
> https://math.stackexchange.com/questions/831768/under-assumption-that-fracm-n1m-n-le-2-what-is-true?lq=1
> > >
> > >
> >
> https://math.stackexchange.com/questions/793555/is-there-a-conjecture-with-maximal-prime-gaps?lq=1
> > >
> > >
> > >  John W. Nicholson
> > >
> > > _______________________________________________
> > >
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