Talk:Twin prime

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[edit] New record twin prime?

On 8 September 2005, 84.130.217.208 updated the "largest known twin prime" here and on Chen prime to record a new record. I've not been able to find any reference to this new record via Google, so I've asked for one on the contributor's talk page, but in the meantime if anyone knows anything about it please shout. Hv 19:40, 8 September 2005 (UTC)

  • I've got good news and bad news. Good news: 1. The entry is correct, 2. I'm delighted the largest known Chen prime is also found, and many people have found Chen primes very interesting. Bad news: We don't know who updated the Twin prime and Chen prime pages to announce this good news. Giftlite 23:28, 8 September 2005 (UTC)
Thanks; I'm kind of surprised there isn't anything found by Google on this, but I guess I shouldn't be. Hv 01:18, 9 September 2005 (UTC)
could have been me. and i just updated to a new alrger prime, though not much larger. they always come here http://primes.utm.edu/top20/page.php?id=1 and are anounced in some yahoo groups. all are verified primes. -thommy

[edit] Factorial

Why is factorial under see also? Ozone 03:13, 2 January 2006 (UTC)

I think because this operator appears in this equation: 4((m-1)! + 1) = -m \mod (m(m+2)). Giftlite 02:27, 1 February 2006 (UTC)
As to that formula, apart from changing the depreciated "proven" to "proved" (according to wiktionary), it would be nice to have a reference for that proof. — MFH:Talk 02:42, 25 March 2008 (UTC)

[edit] Mathematical Definition of Silly

Regarding this edit:

02:53, 8 March 2006 Dmharvey m (remove silly "proof" from external links -- thanks again DYLAN)

What exactly is the definition of 'silly'? Also, while you're at it, please define mathematically 'arrogance'. These are external links, not legal testimony. Please stop squelching any innovation that doesn't fit in to your narrow minded view of mathematics. If you feel you are mathematics' custodian, please fashion yourself a thrown to sit on, only make sure it's located somewhere out on the Atlantic Ocean where we needn't listen to people such as yourself. —The preceding unsigned comment was added by 38.116.204.67 (talk • contribs) 18:46 and 18:51, 13 March 2006 (UTC)

[edit] Merge with Twin prime conjecture?

OK, it's possible to discuss the two topics separately, but is it useful? It's not as though we're hurting for space; the two articles combined come to less than 10K. (BTW there's an inconsistency; twin prime says a twin prime is an individual prime, whereas twin prime conjecture says it's a pair). --Trovatore 21:15, 13 March 2006 (UTC)

I agree. I don't see a good reason to keep the articles separate. The topics are quite intertwined, the twin prime article is barely over stub length, and the contents of the articles overlap. (I fixed the inconsistency.) -- EJ 21:47, 13 March 2006 (UTC)

[edit] Merge with Twin prime conjecture - They're equally stubborn

There are equally self righteous mathematicians goal tending that page. The EXTERNAL LINKS section is intended for EXTERNAL LINKS, not only for published mathematical papers. 38.116.204.67 21:27, 13 March 2006 (UTC)

They are not for published papers, the "references" section is for that.— MFH:Talk 02:42, 25 March 2008 (UTC)
It's not for links to just anything. There's got to be some quality control, or we'll be overrun with links to crackpot sites. I'm not saying that's what your site is; I haven't looked into it that closely. (My first guess is that you may very well have a good, convincing argument in favor of TPC, but you probably don't have an actual proof, and you may not fully understand the difference.) In any case I'd say there's a "rebuttable presumption" against amateur sites. Feel free to have a shot at rebutting it. A good start would be to convince a recognized expert. --Trovatore 21:35, 13 March 2006 (UTC)
Here's a great question for you. Suppose a 32 year old computer scientist has an insight. Suppose that the insight is ground breaking. Suppose that any local expert the computer scientist approaches lacks the insight to see the deeper meanings. Suppose the computer scientist needs to reach a 1 in a million expert. Now suppose that your stubborn refusal blocks this process until long after the computer scientist is dead, and as a result, we never get warp engines, clean power supplies and all those other things that would make the world a nicer place? Think I'm nuts? Look at the connections between the riemann(sp?) and quantum mechanics. Enjoy your particular mountain for as long as you are king of it. —The preceding unsigned comment was added by 72.136.90.95 (talk • contribs) 03:52, 14 March 2006 (UTC)
Independently of any question about insight, there is a basic principle on WP which is called "no original research". This means that you must indeed publish your results elsewhere, and even after this wait until it is "commonly accepted", before putting it here. Feel free to leave a link on this talk page, however, if you feel the urge. — MFH:Talk 02:42, 25 March 2008 (UTC)
I assume you are a 32-year old computer scientist. Have you actually tried asking any "local experts"? (By the way, you might be taken more seriously here if you create an account, and sign your messages with four tildes: ~~~~. It also makes it easier to keep track of the discussion. Thanks.) Dmharvey 14:38, 14 March 2006 (UTC)
But of course. My professor that introduced me to this problem is super busy with no time to talk to me. You see there's nothing in it for them (experts). Suppose I'm right: then all they do is help some other person get credit for a big discovery. Suppose I'm wrong: they've wasted their time. Either way they've done nothing for themselves. It's much easier to dismiss me. I'm trying to find someone who has an open mind for these things. It's very difficult to find. 38.116.204.67 17:24, 14 March 2006 (UTC)
On the other hand, "experts" are the only people who will be able to help you get your ideas recognised. Adding a link to Wikipedia isn't going to help with such recognition. We are, after all, not experts here. There are people here who, like it or not, will revert your link, without some other evidence that the material has been appropriately reviewed. So, some way or another, you're going to need to get some experts to carefully assess your work. I briefly perused the discussion on that newsgroup you posted earlier, and it sounded like some people there had some issues with your conception of probability. Maybe try asking some grad students studying statistics or probability, I assure you that grad students have far more time available than professors :-), and are probably more open-minded too. Dmharvey 17:49, 14 March 2006 (UTC)
Good God, is this what goes on in Mathematics circles outside Humanities faculties? In that case thank goodness I pursued a pure mathematics course because I always found my professors incredibly tolerant of my supposed insights! Just a suggestion, but perhaps they might listen to you more if you couched your brilliant breakthrough in humbler terms? One gets the impression that our friends in the impure sciences :-p seem to forget that ultimately all research is a human endeavour and relies on human interaction at some level to enable progress, and mutual affability expedites the immediate openness of others to one's ideas.Gondooley 11:50, 20 May 2006 (UTC)

[edit] Brun's constant

http://en.wikipedia.org/wiki/Brun's_constant

Prime Twin Constant called the Brun's Constant ! and not 1.3xxxxx

thx

Patrick Bertsch —Preceding unsigned comment added by 134.60.222.1 (talk • contribs) 20:43, January 7, 2007

AFAICS, it's neither that nor the other: it's twice the twin prime constant 0.6601..., cf. Twin prime conjecture (after correcting the product which should run over (all, not only twin-) primes p>3). To get Brun's constant, 1.9..., you sum over twin primes only.— MFH:Talk 02:42, 25 March 2008 (UTC)
As to that formula, I'll add that p must be prime, and from changing the depreciated "proven" to "proved" (I'll fix these two), it would be nice to have a reference for that proof.[cf "Factorial" above] — MFH:Talk 02:42, 25 March 2008 (UTC)

[edit] Pairs that is being discovered

Most of the pairs that is being discovered are of the form (4m-1,4m+1). However, the proof showing there are infinitely many twin primes is not enough to show that there are many pairs of the form (4m-1,4m+1).　It also has not been shown whether the highest pair is of the form (4m+1,4m+3) or (4m-1,4m+1) if there are only finitely many twin primes. 218.133.184.93 19:13, 28 January 2007 (UTC)

No "proof", no reference to a proof. It doesn't belong in the article. — Arthur Rubin | (talk) 18:13, 28 January 2007 (UTC)
Even rather counter-evidence: e.g. in 1e7..2e7 and 2e7..3e7 there are more twins (p,p+2) with p=1 (mod 4) than with p=3. The fact that the largest known twins are of the form k*2^n +/- 1 of course stems from the fact that only numbers of that form have been considered! — MFH:Talk 04:27, 25 March 2008 (UTC)

[edit] Inconsistency?

I'm a little confused by the following two sections:

the number of twin primes less than x is << x/(log x)2.
the number of such pairs less than x is x·f(x)/(log x)2 where f(x) is about 1.7 for small x and decreases to about 1.3 as x tends to infinity.

They seem contradictory to me. Can anyone explain this better either to me or on the page?99of9 (talk) 05:05, 19 February 2008 (UTC)

The explanation is simply that the former statement was in error. Fixed now. -- EJ (talk) 12:56, 19 February 2008 (UTC)
Thanks for fixing. 99of9 (talk) 23:31, 19 February 2008 (UTC)

[edit] Dots in the function statement intended to end the sentence

I'm going to repost my argument from Talk:Collatz conjecture instead of writing the same thing over again.

I see that they're *intended* to end the sentences, but they end up confusing the function declaration. I don't think it's necessary to insert the period - the end of the sentence is implicit by the colon before the declaration and the declaration itself. The periods wind up appearing to be part of the mathematical or logical statement and merely confuse things without making anything more clear. I think we should take them out. Kyle Barbour 07:53, 5 April 2008 (UTC)

O.K. After a looking a bit into other textbooks than mine and a few arXiv papers, I see that this my opinion is not standard, and I retract my argument. :) Kyle Barbour 20:55, 5 April 2008 (UTC)