Talk:Twin prime conjecture/Archive 1

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1

Axel - you've done it again. It is fine to extend articles but please don't cut them. How many See also should be in one article? I guess you chase me to pull mine tail, ha, ha.
XJamRastafire

Well, there's no hard rule how many see also's you need. I thought that we probably won't have separate articles for "twin prime constant" and "Hardy-Littlewood conjecture", since those two topics are now well covered in this article. On the other hand, if we decide to have a separate "Hardy-Littlewood conjecture" article (which might be a good idea), then much of the material now in "Twin Prime Conjecture" should be moved there. AxelBoldt

Yes I see. But this is, I guess, just you opinion. I think we should a little bit think of the future. I am shure that in some 2 or 4 years an article for twin prime conjecture would be extend in, let us say, some great amount. And I have already used a reference for twin prime constant in the article for Brun's constant B and now it is lost because you had deleted it. And furthermore if someone will look for twin prime constant in very extended and 'huge' near-future article Hardest extended twin prime conjecture he would have to work one's way through it. It is a very thin line between encyclopedias, dictionaries and thick books. I hope we all understand each other.
XJamRastafire [2002.02.25] 1 Monday

Axel can you please explain why we don't use a term of logarithmic integral Li(n) and the function Li₂(n)? Are you inventing a new kind of math, perhaps?
XJam [2002.04.02] 2 Tuesday (0)

In the article, we didn't use the function Li₂(x) anywhere but in the one formula, so there was no need to introduce the notation. There is no point in introducing a notation if you're not going to use it; it just confuses the reader. AxelBoldt

Hey man, I don't want to confuse a reader. I just want to give him futher information. It is nice to see that logarithmic integral shows itself in many equations for the density of primes. I am not shure what a term NPOV really means? I give constructive annotations and you obviously deny all of them. I hope I'll still have enough will to continue my work here in Wikipedia. -- XJam [2002.04.02] 2 Tuesday (1st ed)

It is true that I often initially modify or remove additions of yours, because I think they are unclear or for other reasons. But in the end, many Wikipedia math articles have been getting a lot better because of your involvement. AxelBoldt

Yes OK. I am glad then if I can do some improvements on articles. But concerning rigorous definitions I've noticed too that you put out off some article external links as ((Good introductory article on Brun's constant at: http://numbers.computation.free.fr/Constants/Primes/twin.html )) I quite understand that article but if you have problems understanding it, I guess it's your problem. You should ask that writer in what way p in the limit is defined. I don't agree that a series and a constant are the same thing... I do prefer if you first ask what you don't understand and what you think is not right and after that I shall try to fix it up. And thanks for above encouragement anyway. -- XJam [2002.04.02] 2 Tuesday (2nd ed)

That is a good link, I'll put it on twin prime. And it is indeed quite clear. B₂(p) is the sum of the reciprocals of the twin primes up to p. You didn't mention the last part, and without that the definition is not clear. AxelBoldt

AxelBoldt, if something is not clear, make it clear, or discuss it on the talk page. don't ever remove material from a page unless it is patent nonsense. Positive information value should never be removed from a wikipedia article. - Taxman 12:25, Jun 9, 2004 (UTC)

What's up with 80.189.119.162's edits? I'm currently afraid of clicking on the added links. Erzengel 12:39 15 May 2003 (UTC)

Seems crankish, this "J. perry" has a site full of crankish "simple proof of euler thorem", "perry zeta function" "short proof of four color theorem etc." a "James Harris" on Wikipedia?? (be afraid) Rotem Dan 12:58 May 15, 2003 (UTC)

I'm Richard Heylen, an amateur mathematician, and I noticed that J. Perry had boasted about changing the wikipedia page on http://groups.yahoo.com/group/primenumbers/message/12450 I've tweaked this page to better reflect what I think is the reality of the situation but as soon as you've worked out how to stop John posting inappropriate "information" on this page then please delete the whole lot. Thanks! rick DOT heylen AT macrovision DOT com

Proof of this conjecture was submitted last wednesday. I took a glance at it but it is far far far beyond my abilities to understand. I'm only in ODE right now. Anyway, it's located here, if anyone understands it they should write up a summary and include it in the article. --Starx 23:45, 28 May 2004 (UTC)

I suggest much much more carefulness. Apparently Gerard Tenenbaum shares the opinion on problems in the paper.

http://listserv.nodak.edu/scripts/wa.exeA2=ind0406&L=nmbrthry&F=&S=&P=1119

Incidentally the author acknosledges the problem, see the link !, so my best suggestion is to remove the WHOLE MATERIAL on the purported proof.

No, it, just like Wiles' initially flawed proof of Fermat's last theorem, may be repaired. For a potential proof for a problem of this magnitude by a very well respected mathematician, I think it sufficient to note there are problems with the proof that the author acknowledges, and that may or may not be able to be fixed. Btw, where do you see that the author acknowledges the problem? Also, that link doesn't work directly for me for some reason. - Taxman 12:25, Jun 9, 2004 (UTC)

You can try this http://arxiv.org/abs/math.NT/0405509 (in case you cannot get it, the author says "A serious error has been found in the paper, specifically, Lemma 8 is incorrect." ) I don't want to compare him to Wiles but I think in the period when Wiles had problems with the proof he still had a theorem, only his theorem then did not include the case needed for FLT. Here there is no theorem.

Ok, edited the article to note the withdrawn proof and link to the counterexample that Tenenbaum provides, but maintained the information on the potential proof and its having failed. - Taxman 15:17, Jun 9, 2004 (UTC)

It's Yıldırım, not Yildirim

Ok, and that is easy enough to fix. Do you have some solid evidence that that is the correct way to write the name? - Taxman ^Talk 18:13, Jun 6, 2005 (UTC)

That's the way it's spelt on his home-page [1]. I was the one who entered in the name; I was too lazy to do it correctly earlier but I can cut and paste it in now :-). Terry 21:01, 6 Jun 2005 (UTC)

Could anyone please tell me, who's a bit of a loser in mathematics, why p' − p < c ln p together with the fact, that c may be arbitrarily small, doesn't lead to infinitely many twins? Thank you. --FAeR 05:02, 14 December 2005 (UTC)

p and p′ are not necessarily twin primes. p′ is just the next prime after p. What these results say is that there are infinitely many primes whose prime successor is not "too far away" from the given prime. Unfortunately, even if you choose c very small, c ln p can still become greater than 2 as p gets large — that's the rub. - Gauge 04:54, 19 December 2005 (UTC)

Is there any reason Gödel's incompleteness theorem is linked to?