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There are the obvious reasons why a question is not well-received:

  • User just copied a question from homework or a textbook and doesn't explain.
  • A question is unclear
  • A question has been asked a million times and the answer is available if a person just reviewed the Similar Questions section.
  • A question is off-topic (it's a physics question or programming question)

A little bit about my question.

I was exploring the frequency of twin primes when I notice that for $x > 1330$, the number of twin primes between successive squares (between $36$ and $49$, $49$ and $64$, $64$ and $81$, etc.) was increasing both in terms of the maximum number and the mininum number of twin primes found (By minimum, I just meant that after I found $35$ twin primes between two successive squares, I would see that the minimum number of twin primes found would be at least $\left\lfloor\dfrac{35}{3}\right\rfloor = 11$). I realized shortly after posting the question that I had asked a similar question a year ago.

Someone upvoted me so I decided that I wouldn't delete it since there were differences between the two questions. Last year, I asked about the frequency of twin primes between the squares of successive primes and this year, I asked about the frequency of twin primes between squares of successive integers.

Perhaps, the right thing to do is to delete the question. I will probably do this anyway.

Before I do this, though, I wanted to understand why folks seemed to be very unhappy with my second question. I do not believe that the issue is the similarity to the previous question.

One person has voted to closed the question because it is off-topic because:

This question does not appear to be about math within the scope defined in the help center.

That's a very good reason to close the question if that person is right. To the best of my judgment, I don't see how he is.

My question reports on the results that I found. That for $x > 122$, for all the numbers that I checked, all successive squares of integers have at least one twin prime between their values. For $x > 1330$, the minimum number of twin primes found also increases as the highest number found increases.

I consider this a fair question for this site because empirical results without proofs are often wrong and one of the most interesting insights of mathematics, in my opinion, is when these empirical results are wrong.

I suspect that either my point is not clear or I am asking something very stupid. If my point is not clear, I am very glad to reword the question to make it clear. If my question is stupid, then I really want to understand why. In this case, there is some very fundamental point that I have not yet learned about or I am not adequately applying my knowledge to this issue.

I would greatly appreciate it if someone here could comment on how to figure out when your question is unclear, when it is a dumb question, or when it is better not to ask a question.

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    $\begingroup$ It is a bit tangential, but out of curiosity: what is the motivation or what are you trying to achieve? (I mean with the math, not the meta question.) $\endgroup$ – quid Mar 15 '15 at 14:32
  • $\begingroup$ I really enjoying thinking about logical puzzles and the distribution of primes. In the case of twin primes, I am especially interested in understanding the implications of the fact that sum of the reciprocals of twin primes is convergent. How can that be? What does that imply about the distribution of twin primes if they are truly infinite as everyone believes. $\endgroup$ – Larry Freeman Mar 15 '15 at 14:52
  • $\begingroup$ @quid, Thanks very much for the well-written and informative answer. You gave me exactly what I was looking for. Cheers! :-) $\endgroup$ – Larry Freeman Mar 15 '15 at 19:01
  • $\begingroup$ You are welcome. Thanks for you reply, too. $\endgroup$ – quid Mar 15 '15 at 19:15
  • $\begingroup$ @LarryFreeman reciprocals of $2^n$ are infinite, are they not? They are just not very dense... $\endgroup$ – martin Mar 18 '15 at 8:46
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    $\begingroup$ Hi @Martin, that's the type of analogue that I am looking for as a way of understanding of what's happening with the twin primes. I think my issue is that I did a very poor job of asking my original question. So, my question was very unclear. $\endgroup$ – Larry Freeman Mar 18 '15 at 14:05
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I think I understood what you were getting at in the question, and think it's basically a fine question (I was just asked to vote on whether it should be closed and said no).

But it could be more clearly and concisely asked, and I can understand people thinking it unclear.

If I'd asked the question, I'd have written something like:

"Let $a(n)$ be the number of pairs of twin primes between $n^2$ and $(n+1)^2$. Of course, if the twin primes conjecture is false then $a(n)$ is zero for large $n$. But is anything known or conjectured about the behaviour of $a(n)$ as $n\to\infty$?

For example, is it known or conjectured whether $a(n)$ is bounded? Or whether it tends to infinity?"

And then I might have added something about what your computer experiments suggest. Maybe it's just me, but I generally find that my attention is grabbed more by a question followed by some data (whose significance is easier to appreciate when I'm already thinking about the question), than some data (leading me who knows where) followed by a question.

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    $\begingroup$ Thank you very much! I think that your version of the question is quite clear and vastly superior to my wording. I really appreciate this feedback. I will keep this in mind as I ask my future questions. Cheers! :-) Am I allowed to change my wording to use yours instead? $\endgroup$ – Larry Freeman Mar 15 '15 at 14:54
  • $\begingroup$ you can certainly change the wording, maybe with a link to this answer. $\endgroup$ – kjetil b halvorsen Mar 24 '15 at 19:38
  • $\begingroup$ Thanks @kjetil. I ended up adding a block quote to my question which quotes Jeremy. $\endgroup$ – Larry Freeman Mar 25 '15 at 15:53

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