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@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....
@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).
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.
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
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.
Dear MO Scribe,
Nice to have you aboard!
@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?
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."
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
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
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.
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
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
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?
I request that this meta thread be closed.
Seconded.
Thirded.
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