tea.mathoverflow.net - Discussion Feed (reopen one question about twin primes)

José Figueroa comments on "reopen one question about twin primes" (12169)

José Figueroa — Wed, 22 Dec 2010 18:41:05 -0800

Thirded.

Pete L. Clark comments on "reopen one question about twin primes" (12168)

Pete L. Clark — Wed, 22 Dec 2010 18:09:32 -0800

Seconded.

Alex Bartel comments on "reopen one question about twin primes" (12167)

Alex Bartel — Wed, 22 Dec 2010 17:14:35 -0800

I request that this meta thread be closed.

minasteris comments on "reopen one question about twin primes" (12166)

minasteris — Wed, 22 Dec 2010 14:57:31 -0800

my question is not interesting

MO Scribe comments on "reopen one question about twin primes" (12165)

MO Scribe — Wed, 22 Dec 2010 14:43:17 -0800

You can keep repeating 'till the cows come home that your question is interesting, but de gustibus non disputandum est.

minasteris comments on "reopen one question about twin primes" (12164)

minasteris — Wed, 22 Dec 2010 14:32:32 -0800

I just want to see a proof for some values of a. Furthermore it is a little bit unfair to have closed the original question that is really interesting and can give good thoughts such as these that MO Scribe asked
thank you

MO Scribe comments on "reopen one question about twin primes" (12163)

MO Scribe — Wed, 22 Dec 2010 14:20:29 -0800

@Anton, if you decide to open the question again, could you at least phrase it in the following way:

Given a positive integer $a \ge 3$, do there exist infinitely many integers $k$ such that:
1. $ak+1$ has no non-trivial factors of the form $\pm 1 \mod a$,
2. $ak-1$ has no non-trivial factors of the form $\pm 1 \mod a$.

If $a = 3$, $4$, or $6$, this is equivalent to the twin prime conjecture, because, in those cases, EVERY non-trivial factor of a number co-prime to $a$ is of the form $\pm 1 \mod a$, since $\phi(a) = 2$. However, in general, it is a weaker problem. Since one expects there to be infinitely many twin primes of the form $p$, $p+2$ with $p \equiv -1 \mod a$, one also expects that there are infinitely many such $k$ for every $a$. However, is it possible that one could prove this _unconditionally_ for some (any) value of $a$?

****

I honestly don't think asking such a question will provide any added benefit beyond the question that I asked. If it's not phrased in this way, but rather in terms of the exceedingly awkward and potentially ambiguous $amn \pm m \pm n$, that just leaves open the chance that someone will misread the question, becoming confused and answer a different question. As a general warning, one can ask endlessly difficult but fundamentally uninteresting questions about prime numbers, and I would prefer that a higher proportion of such questions actually have some connection to what number theorists (i.e. the target of MO) actually think about rather than just be unmotivated difficult (or not) problems. (That's not that number theorists don't think about prime numbers - for a sense of what I am trying to say, it's probably better just to compare the original question (or even the version above) to the one I posted, which tried to add some context to the problem.)

Anton Geraschenko comments on "reopen one question about twin primes" (12161)

Anton Geraschenko — Wed, 22 Dec 2010 13:08:02 -0800

From Matt's answer on math.SE:

So what is the conclusion: Well, there is no doubt that one should be able to find infintely many such k, since it follows from standard conjectures on twin primes satisfying congruence conditions. On the other hand, proving this may be tricky, since it seems to require results that are at the edge of what is currently possible via seiving techniques.

In light of the non-triviality of the question and the (well-formated and properly capitalized) additional motivation provided by the OP, I think it makes sense to reopen the second incarnation of the question (and clear the comments related to its closure):
http://mathoverflow.net/questions/50159/do-we-have-a-proof-of-the-infinitness-closed

As far as I can tell, the question is not subsumed by MO Scribe's question. It may be that the reopened question won't get any answers, but it seems like the arguments for closing the question no longer apply. Am I missing something important?

minasteris comments on "reopen one question about twin primes" (12160)

minasteris — Wed, 22 Dec 2010 11:50:23 -0800

http://math.stackexchange.com/questions/15075/do-we-have-a-proof-of-the-infiniteness

minasteris comments on "reopen one question about twin primes" (12152)

minasteris — Wed, 22 Dec 2010 10:45:19 -0800

Sorry if I was rude.

Emerton comments on "reopen one question about twin primes" (12151)

Emerton — Wed, 22 Dec 2010 08:31:11 -0800

Dear Minasteris,

As far as I can tell, I've answered your question with my post at Math.SE, and, unless I've made a mistake (always possible!) the answer is straightforward. So I don't see any reason for it to be posted on MO. Let's please stop discussing it here now, and have any further discussion over at Math.SE.

Regards,

Matt

minasteris comments on "reopen one question about twin primes" (12150)

minasteris — Wed, 22 Dec 2010 08:27:08 -0800

Maybe it is not a good question at last ,thank you for your time.

minasteris comments on "reopen one question about twin primes" (12149)

minasteris — Wed, 22 Dec 2010 08:23:24 -0800

Dear Matt,
I will be happy if i have answers anywhere .I just want to know what do we know about this .The reason that i insisted to ask it at MO is that I was thinking that is more possible to have an answer here because this site is visited by more and maybe more advanced mathematicians.But I think that this question would be perfect for MO because it is of research level(it has really difficult parts) .Please write your opinion about, thanks in advance.

Emerton comments on "reopen one question about twin primes" (12148)

Emerton — Wed, 22 Dec 2010 08:15:17 -0800

Dear Minasteris,

Since your question now seems to be living on Math.SE, rather than on MO, it's probably best to have any further discussions about it over there.

Regards,

Matt

minasteris comments on "reopen one question about twin primes" (12147)

minasteris — Wed, 22 Dec 2010 08:13:21 -0800

what if a is prime?

minasteris comments on "reopen one question about twin primes" (12146)

minasteris — Wed, 22 Dec 2010 08:09:16 -0800

Thank you very much.

Emerton comments on "reopen one question about twin primes" (12145)

Emerton — Wed, 22 Dec 2010 07:58:57 -0800

Dear Minasteris,

Math.SE is shorthand for math.stackexchange.com.

Regards,

Matt

P.S. Your question was closed at MO and the latest version will surely be closed as an exact duplicate. Thus it seems more appropriate to answer your question at math.stackexchange than here at MO.

minasteris comments on "reopen one question about twin primes" (12144)

minasteris — Wed, 22 Dec 2010 07:58:30 -0800

I have reasked it at MO so could you give an answer there?

minasteris comments on "reopen one question about twin primes" (12143)

minasteris — Wed, 22 Dec 2010 07:55:45 -0800

Dear Matt
How can i get to math.se. please give me a link, thanks in regards.

Emerton comments on "reopen one question about twin primes" (12142)

Emerton — Wed, 22 Dec 2010 07:52:40 -0800

Dear Pete,

I thought more about the question, and so I happily retract my request for you to explain your remark. Sorry to have bothered you with it at all; I just wanted to try to resolve this issue in a positive way.

Dear Minasteris,

I've posted an answer to your question on Math.SE.

Regards,

Matt

minasteris comments on "reopen one question about twin primes" (12141)

minasteris — Wed, 22 Dec 2010 07:31:04 -0800

I would be pleased if Pete L.Clark give the proof That Emerton asked here,thank you.

minasteris comments on "reopen one question about twin primes" (12140)

minasteris — Wed, 22 Dec 2010 07:24:31 -0800

So Emerton you say that it is an open problem for all the values of a because that is my question.

Emerton comments on "reopen one question about twin primes" (12139)

Emerton — Wed, 22 Dec 2010 07:18:37 -0800

Dear Minasteris,

Did you read the comments by MO Scribe at all? As is explained in them (and in the question that MO Scribe posted which was inspired by yours), your question is expected to have a positive answer, but it may be difficult to prove this.

Dear Pete,

Could you say a word about how "It is easy to see ...", if not here than maybe on Math.SE; it would be good if this could be resolved in a way that is at least somewhat satisfying for everyone, and giving an answer would surely be the easiest way to do this.

Best wishes,

Matt

minasteris comments on "reopen one question about twin primes" (12126)

minasteris — Tue, 21 Dec 2010 09:37:19 -0800

I put the question in math.stackexchange .Lets see if I will get at last any answer, but how a question that MO cant answer will be answered by mathstackexchange? if you have any answer here i am still waiting...

Ben Webster comments on "reopen one question about twin primes" (12099)

Ben Webster — Mon, 20 Dec 2010 19:42:27 -0800

By the way, while I feel almost as sheepish about this as Theo apparently does: MO and meta.MO are professional fora. This is not why your questions have been closed, but I assure you things will go more smoothly if you write in full English sentences which are spelled and punctuated with some approximation of correctness, instead of writing things like "ok thnx."

Pete L. Clark comments on "reopen one question about twin primes" (12097)

Pete L. Clark — Mon, 20 Dec 2010 19:18:20 -0800

@minasteris: My comment on the question pertains to version 3 in the edit history, where the formatting makes it look like you are asking about the expression $anm \pm n \pm nm$. It is easy to see that if a is sufficiently large, there are infinitely many primes not represented by this expression.

If you are still interested in the question, why have you not reposted it on math.stackexchange.com, as has been recommended to you several times?

minasteris comments on "reopen one question about twin primes" (12086)

minasteris — Mon, 20 Dec 2010 13:43:56 -0800

MO Scribe.It is obvious to me that the conjectural answer is that for any a we should have infinitely many not of the form that i gave, numbers. But my question is : do we have a proof for some a as Pete .L.Clark claimed to my first question http://mathoverflow.net/questions/49647/finite-or-infinite-closed. I understand that you are saying that we don't have .( or not? )please answer analytically because my english are not so good.Thanx for your time.

minasteris comments on "reopen one question about twin primes" (12081)

minasteris — Mon, 20 Dec 2010 12:10:49 -0800

ok thnx

Harry Gindi comments on "reopen one question about twin primes" (12075)

Harry Gindi — Mon, 20 Dec 2010 10:40:57 -0800

Dear MO Scribe,

Nice to have you aboard!

MO Scribe comments on "reopen one question about twin primes" (12074)

MO Scribe — Mon, 20 Dec 2010 10:38:29 -0800

@minasteris, since you 1.Don't seem to understand my remarks about your problem above, and 2. Haven't given any indication of your background (I'm going to continue to assume at this point that you are an undergraduate), my recommendation is no, don't post the same question again.

Just to repeat what I have said at least twice:
1. It is a completely standard conjecture that there are infinitely many twin primes of the form an+1,an-1. This implies that the CONJECTURAL answer to your question is: For ALL a at least 3, there are INFINITELY many numbers not represented by the given form.

The question as to whether one can provide UNCONDITIONAL results towards your problem is exactly what is addressed in my question.
None of this will be in any way useful for studying twin primes.

minasteris comments on "reopen one question about twin primes" (12066)

minasteris — Mon, 20 Dec 2010 09:08:08 -0800

so do you think that i should try to post this question again in a better form or not? Because i really want to know the answer and yet I do not.

Todd Trimble comments on "reopen one question about twin primes" (12064)

Todd Trimble — Mon, 20 Dec 2010 09:02:58 -0800

I agree, Theo. There was a recent question (tagged category theory) where, even allowing that the OP is not a native speaker of English, was incredibly sloppy (caps in odd places, endings of sentences left off) before people stepped in to edit. It's hard to want to put care and consideration into an answer when the original question is poorly composed and hard to read.

theojf comments on "reopen one question about twin primes" (12037)

theojf — Sun, 19 Dec 2010 19:51:59 -0800

Dear minasteris,

I hope the following request does not come across as rude --- I mean it in the kindest way. I have found some of your posts difficult to read only because they do not follow standard English capitalization rules. Although it is probably unfair, I think that many people do evaluate how seriously to take a post or comment based on such things. I don't think your mathematical questions are at all poor, but without knowing more about you, I and I bet many other people here will respect your questions more if you adopt a more copy-edited voice in your online writing. So my request is: please capitalize carefully?

-Theo

minasteris comments on "reopen one question about twin primes" (11997)

minasteris — Sat, 18 Dec 2010 10:10:13 -0800

mo scribe I voted too for your question but do you mean that the answer for any a is known? Do we have a proof for some a as Todd questioned? Maybe the different values for a makes it easier to be answered than for value 6( twin prim conjecture). If we could have proofs for some values maybe we could have a method? do you think that i should set the question again providing more information? but the question was: by the methods that we have can we have a proof for a=100 as Pete l. Clark said in a comment to my first question? do we have an answer for 30 etc. that is a kind of reverse question about twin primes? so would it be useful to make this question or it will be closed again and i will not accept any answer ?

MO Scribe comments on "reopen one question about twin primes" (11996)

MO Scribe — Sat, 18 Dec 2010 09:51:13 -0800

Dear minasteris, I want to explain why your question was not appreciated, in case you decide to ask any further questions. General remarks along these lines are surely in the FAQ, but let me be very specific about your particular question.

1. There was no background on the problem: Why is this problem interesting? Why not write down the identity $a(amn \pm m \pm n) = (am \pm 1)(an \pm 1) \pm 1$ connecting the problem to factorization of pairs of integers $(ak-1,ak+1)$?

2. There was no background on _you_: Are you an undergraduate playing around with elementary expressions? Do you know the standard conjectures about primes, say, the Hardy-Littlewood conjecture? Anything about sieving (in the modern sense)? Perhaps most importantly: what methods have you tried so far?

3. You weren't very clear on what type of answer you were looking for: As I remark early on in my re-write, it follows from completely standard conjectures that the answer will be yes for all $a$. It's certainly not clear from your question whether you expected or knew this, nor whether this remark would be an acceptable answer to you or not.

4. You made typos in your original question. Your original formulation, I believe, omitted the condition that $n$ and $m$ were not zero. Surely that was a typo. Yet IF you had given more information (along the lines of 1 or 2 above), the readers might have been able to work out what you were trying to ask. As it was, your failure to do this meant that people did not give you the benefit of the doubt.

My impression is that you are an undergraduate playing around with prime numbers, and if so, great! But a general remark (not specifically to you): there are lots of random questions that could be (many have) asked on MO about prime numbers. Most questions are very hard, although they often follow from standard conjectures. Honestly, your problem (correctly formulated) seems pretty random to me. What is perhaps more interesting are the _methods_ used to study such problems, and the limitations of those methods. The reason people voted up my rewrite has less to do with the original question and more to do with a genuine mathematical issue: can one combine two specific sieving problems simultaneously.

Todd Trimble comments on "reopen one question about twin primes" (11995)

Todd Trimble — Sat, 18 Dec 2010 06:54:52 -0800

Upon further reflection, it seems to me that minasteris's repreatedly-asked question (under the moniker asterios gatzounis) is not at all trivial. I accept in particular the argument this individual gives (as an answer to MO Scribe's question) that if $N$ is not of the form $6mn \pm m \pm n$, then both $6N+1$ and $6N-1$ are prime, and I am not seeing an easy argument for why there exists some $a$ such that there exist infinitely many numbers not of the form $amn \pm m \pm n$. For example, I think I can give a heuristic argument that for any given $a$, the density of numbers of this form is 1.

So, these questions might be open problems. If they are known to be open problems (as in the case $a = 6$), then that in itself rules out their appropriateness as MO questions, but I don't know the status of these things. I think that if minasteris asked again, presenting his argument that the case $a = 6$ is linked to the twin primes conjecture, and then asked whether there is any $a$ for which it is known that there are infinitely many numbers not of the form above, then that is a perfectly fine question, and I cannot see why this should be summarily closed without further discussion.

minasteris comments on "reopen one question about twin primes" (11994)

minasteris — Sat, 18 Dec 2010 00:23:39 -0800

i repost an answer that i've gotten :The question has been closed. It is not of research level. It would however be quite appropriate at math.stackexchange.com, and I invite you to repost it there. (To answer the question of your last comment: yes.) – Pete L. Clark yesterday

minasteris comments on "reopen one question about twin primes" (11993)

minasteris — Fri, 17 Dec 2010 23:28:21 -0800

but it is the same in a more analytical way

minasteris comments on "reopen one question about twin primes" (11992)

minasteris — Fri, 17 Dec 2010 23:07:36 -0800

so i should have written it analytically

WillieWong comments on "reopen one question about twin primes" (11985)

WillieWong — Fri, 17 Dec 2010 12:37:12 -0800

@MO Scribe: my opinion is that you can leave it as it is. It should be completely reasonable to ask a question inspired by some other question (so long as it is not an exact/close-enough duplicate).

MO Scribe comments on "reopen one question about twin primes" (11984)

MO Scribe — Fri, 17 Dec 2010 12:24:32 -0800

Since I could detect the germ of an interesting question, I unilaterally re-wrote it myself and posted it here:

http://mathoverflow.net/questions/49751/chens-theorem-with-congruence-conditions

I hope this is OK. One thing I wasn't sure about: should I make the question community wiki? It's not really my question (in some sense), but the question itself is not really a soft-question.

WillieWong comments on "reopen one question about twin primes" (11980)

WillieWong — Fri, 17 Dec 2010 09:20:17 -0800

@Noah, I think the OP is asking about this question and its follow up.

@minasteris: you wrote:

I think that it should be re-opened because it is interesting.

That is evidently a true statement considering that you've asked it three times now. But also evident is the fact that some people consider the question un-interesting. A word of advice: if you want the question re-opened, you should put forth a more convincing argument than what is rather self-evident. Perhaps, if you elaborate a bit more on the connection with twin-primes etc....

minasteris comments on "reopen one question about twin primes" (11979)

minasteris — Fri, 17 Dec 2010 08:45:28 -0800

http://mathoverflow.net/users/11564/asterios-gantzounis

minasteris comments on "reopen one question about twin primes" (11978)

minasteris — Fri, 17 Dec 2010 08:43:08 -0800

what link?

Noah Snyder comments on "reopen one question about twin primes" (11977)

Noah Snyder — Fri, 17 Dec 2010 08:41:29 -0800

You should put a link to the question.

minasteris comments on "reopen one question about twin primes" (11976)

minasteris — Fri, 17 Dec 2010 08:33:33 -0800

i want to see the probable answer or what do we know to this direction,if there is a general method attacking these questions etc.

minasteris comments on "reopen one question about twin primes" (11975)

minasteris — Fri, 17 Dec 2010 08:24:47 -0800

yesterday i asked a question about finite or infinite of one relation and MO closed it as very easy, but it is not easy ,if you put a=6 it is equivalent to the twin prime number conjecture.I asked today again about what about the other values of a and MO closed it again.i think that it should be reopened because it is interesting http://mathoverflow.net/users/11564/asterios-gantzounis or http://mathoverflow.net/questions/49730/twin-primes-etc-closed