Wikipedia:Articles for deletion/Carol number


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was   no consensus.

Consensus is not clear here, hence the close. Even those advocating keep admit mostly that the notability is weak but yet exists. While this means that the article will not be deleted at the moment, it also means that there was no consensus to keep it, just none at all. Merging this and other similar articles into a new article seems to be a possible solution on which people !voting both keep and delete seem to be able to live with. Regards  So Why  09:31, 3 February 2009 (UTC)

Carol number

 * ( [ delete] ) – (View AfD) (View log)

Deprodded. Sources do not indicate notability (mostly just briefly mention it), talk page discussion of "What's the point of this?" has been stalled for years. Reason that this formula is important or useful has never been shown. - Richfife (talk) 06:23, 28 January 2009 (UTC)
 * I'll leave this one to the mathematicians and recommend no action is taken until experts have looked at this and commented on this debate page. - Mgm|(talk) 11:26, 28 January 2009 (UTC)
 * Comment I have notified Wikipedia talk:WikiProject Mathematics. Gandalf61 (talk) 11:54, 28 January 2009 (UTC)


 * Strong keep - appearances in OEIS, MathWorld and Prime Pages establish notability when taken together. Point is that Carol numbers are a hunting ground for large prime hunters. No need to show that they are "important or useful" - if these were key inclusion criteria, then half of Wikipedia would disappear ! Gandalf61 (talk) 11:50, 28 January 2009 (UTC)
 * OEIS is huge and cannot be used to establish notability. Prime Pages does not even discuss Carol numbers, the references are to two specific prime numbers that happen to be Carol numbers, but that's not mentioned there, at most hinted at in the "Description:" formula. MathWorld has seriously downgraded the discussion of these numbers; they used to have their own entries, but this error has now been corrected. See Talk:Carol number. --Hans Adler (talk) 12:18, 28 January 2009 (UTC)
 * Comment Prime Pages contributors use the term "Carol prime" or similar here, here,  here and here. I agree that any one of the three sources (OEIS, MW, Prime Pages) may not be enough to establish notability on its own, but my point is that notability is established by all three sources taken together. Gandalf61 (talk) 12:37, 28 January 2009 (UTC)


 * Strong keep - see this and this. If you google "Carol number", you should get a lot more results. Or I might as well list:, ,and . Definite speedy keep. And the article is still expanding; give it some more time and it should be up to standard. Many articles in WP don't explain importance or notability but that does not imply that the concept is not notable or important!-- PS T  12:08, 28 January 2009 (UTC)


 * Several of those links are merely mirrors of Wikipedia... and none of them is a link to a published paper. I would really like to see a peer-reviewed paper on the topic to establish notability. &mdash; Carl (CBM · talk) 12:27, 28 January 2009 (UTC)


 * (ec x 2) The two Mathworld links are equivalent to the redirects that remain in Wikipedia when an article is merged into another for lack of notability. Why this was done is explained on Talk:Carol number. As to the other four sources you list: is a copy of the old MathWorld entry, from before it was deleted for lack of notability.  is user generated content from Planet Math and cannot be used to establish notability any more than French Wikipedia articles on a topic.  is from Nation Master, a well known Wikipedia mirror.  is really absurd: A machine-generated translation of fr:Nombre Carol. (An amazing business model.) --Hans Adler (talk) 12:30, 28 January 2009 (UTC)


 * Delete Just not enough independent sources. Outside of refs above and wikipedia mirrors I'm having a hard time find references to the sequence. Google Scholar does not give any significant hits. So do these numbers have a wider significance? --Salix (talk): 12:28, 28 January 2009 (UTC)


 * Comment. Two things.  First of all, there appear to be no relevant Scholar hits, nor Google books hits for "Carol number".  Secondly, if this article is deleted, then Kynea number should be deleted as well.   siℓℓy rabbit  (  talk  ) 14:13, 28 January 2009 (UTC)
 * Weak keep per Gandalf61's reasoning. Prime Pages plus MathWorld signifies notability, and the OEIS is another source. A journal paper would be nice, but it's not needed as such. CRGreathouse (t | c) 14:44, 28 January 2009 (UTC)
 * Merge to Near-square prime per Gandalf61's new suggestion. CRGreathouse (t | c) 17:12, 29 January 2009 (UTC)


 * Weak delete as non-notable neologism with too little in non-trivial reliable sources. These numbers were named on a mail list in 2002 by Cletus Emmanuel, an apparently unpublished amateur mathematician who gave the false impression that the names were existing. Two years later he revealed that he named them after a personal acquaintance with no known relation to the numbers or mathematics. The MathWorld editor Eric Weisstein was on the mail list  and created a small MathWorld article, but after learning the real history of the numbers he redirected the name to a broader article which has one paragraph about such numbers without naming them. Weisstein also submitted the numbers to OEIS which has around 154000 integer sequences and accepts almost any submission from the public, for example lots of sequences with numbers belonging to unnamed non-notable polynomials with small coefficients. Some other members of the mail list (maybe also believing it was a seriously named and studied form) searched for primes of this form and found some among the 5000 largest known primes. This automatically qualifies the primes for the Prime Pages regardless of form, but the Prime Pages editor does not name them and for example has no entry at http://primes.utm.edu/top20/index.php or http://primes.utm.edu/glossary/index.php?match=c. Emmanuel has been talking about making a paper for years but as far as I know, he or the numbers have never been published or mentioned in a journal. They appear to remain little known outside the readers of the mail list. PrimeHunter (talk) 15:17, 28 January 2009 (UTC)
 * Comment - minor correction - the MathWorld page does name the numbers - it says they were "arbitrarily dubbed Carol primes by their original investigator in reference to a personal acquaintance" (and it has a similar comment for Kynea primes). I am curious why we should expect academic references for Carol numbers and Kynea numbers when we do not demand them for other similar topics such as Cuban primes and sexy primes - are we suddenly moving the notability bar up a notch here ? Gandalf61 (talk) 15:32, 28 January 2009 (UTC)
 * WP:OTHERSTUFFEXISTS. To reiterate, it appears that Cletus Emmanuel (a non-notable math fan) created this term in honor of a personal friend and began using it as agressively as possible in the hopes that it would stick.  Almost any formula you can dream up will generate primes from time to time.  Again, why is this one special beyond the fact that the creator has written a lot about it?  It's very easy for some with a lot of spare time to submit over and over to non peer-reviewed publications until it seems like they're a crowd.  This is a classic example of Astroturfing.  - Richfife (talk) 16:22, 28 January 2009 (UTC)
 * Comment The terminology is not unique to its originator - the sources show that the terms "Carol prime" and "Kynea prime" are in general use by members of the prime hunting community, including Caldwell, Phil Carmody and Steven Harvey. Since prime hunters are searching for large primes with this form (probably because they suit certain methods of proving primality) then they need to give them some label - the "arbitrary" origin of the names is irrelevant. And there is no requirement to prove that anything on Wikipedia is "special", only that it is notable. Gandalf61 (talk) 17:02, 28 January 2009 (UTC)
 * Which sources? Going down the links in order:  1) Is a self written bio page  2) Is a confession by Emmanuel  3) Doesn't contain the word "Carol" at all  4) is a free webhosted page of uncertain ancestory  5 and 6) Non peer reviewed, user submitted content.  It's not clear that the page is edited at all.  EL 1) Not mentioned until deep into the page and then very half heartedly. EL 2 and 3)  Word "Carol" does not appear at all.  I'm going to remove the three links that don't mention the subject at all, so the indices may move. - Richfife (talk) 17:14, 28 January 2009 (UTC)
 * Comment The links that you have removed concern large proved primes of the form described in the article. Those pages still speak to the notability of the article's subject, even if they do not use the term "Carol prime". I don't think it is reasonable to remove relevant links from an article after you have nominated it for AfD on the grounds that its subject is not notable. Gandalf61 (talk) 17:32, 28 January 2009 (UTC)
 * (Reverted) Re: "probably because they suit certain methods of proving primality". Do you have any evidence of this?  There seem to be a lot of "people smarter than us seem to like this" vibes floating around.  That is actually a valid reason to keep.  If it is true.  But if the smart people have good reasons to use the series, they need to speak up about it.  WP:VERIFIABILITY. - Richfife (talk) 18:03, 28 January 2009 (UTC)
 * Comment Let me explain. If k is a Carol number the k+1 has factors 2n+1 and 2n-1-1. If k+1 is easily factorised then k is well suited to primality tests based on Lucas sequences - see here for details. These "smart people" who search for large primes don't just pick their targets at random, you know. Gandalf61 (talk) 22:55, 28 January 2009 (UTC)

I struck through my above comment of "Strong keep" as User:Hans Adler convinced me otherwise. I think I will stick to a keep but I agree that we need a publication on this (by the way, we don't seem to have any publications on the above mentioned articles (by User:Gandalf61) so I don't see why it is absolutely necessary to have a publication but at least it will clear up some doubts). -- PS T  16:59, 28 January 2009 (UTC)

Delete. An entry in OEIS means nothing. They accept literally anything. I knew someone that was on the editorial board for years, and as long as the sequence made sense (perhaps after intensive inquiry and fixing by him), it would get included. So there are only two sources. MathWorld and Prime Pages. The first means nothing also, particularly given Weinstein's mistaken impression about notability from the mailing list mentioned by Primehunter, someone who, incidentally, knows quite a bit about finding primes. As for Prime Pages, I don't know about the notability of a mention there, but according to what Primehunter said, it only gets mentioned there because some people on the mailing list searched and found some. certainly there is nothing to justify the claim that carol numbers "suit certain methods of proving primality" or are a "hunting ground for large prime hunters" (anymore than any collection of 'not obviously composite' numbers is a hunting ground'). Such claims should be justified by either personal expertise or by reputable sourcing. I see neither. --C S (talk) 18:54, 28 January 2009 (UTC)


 * Delete Fails WP:N. Non-refereed websites, or math hobbiest websites no more authoritative than Wikipedia itself are not sufficient sourcing. "Other stuff exists" and "I like it" are not convincing arguments for neologism articles about types of numbers. What is needed is significant or substantial coverage in multiple reliable and independent sources. The fact that someone feels "Carol (name redacted) is my best female friend in the whole wide world." and wants to name something after her is as irrelevant to the purposes of Wikipedia as would be someone paying a "star registry" to name a star after his Aunt Gertrude, and then someone putting as article about the star "Aunt Gertrude" in Wikipedia. The star registry companies are missing a bet: they could just make up some formula like this with some variation which selects some of the prime numbers then sell a beautiful parchment printout of the "Aunt Gertrude numbers," if the formula generates any, and wait for people to create a Wikipedia article about them. Edison (talk) 18:51, 28 January 2009 (UTC)


 * Keep - as per Gandalf61's arguments. JocK (talk) 02:41, 29 January 2009 (UTC)
 * Delete. For most obscure math topics such as this I'd be happy to !vote keep if I could find three professionally published papers by independent groups on the subject, but this one doesn't even seem to have a single reliable source. And there's nothing particularly faulty about the math in the article, but there's nothing particularly interesting enough either (as evidenced by the fact that in the six or so years since they were named, nobody else has taken the trouble to write and publish any research about them). —David Eppstein (talk) 02:55, 29 January 2009 (UTC)
 * Comment. The MathWorld page doesn't say Carol number. It mentions the name Carol primes but doesn't indicate it's a generally used name. The page only says in a parenthetical remark: "(arbitrarily dubbed Carol primes by their original investigator in reference to a personal acquaintance)". Many prime searchers prefer searches which can get primes on the Prime Pages list of the 5000 largest known primes. In order to prove primality with known methods, a top-5000 prime N must in practice have a form where a large part of the prime factorization of N-1 or N+1 is known. Carol numbers is one such form. It's trivial to create others by multiplying known primes together and adding or subtracting 1. People have searched many forms. There is no reason to think Carol numbers are better suited for prime searching than lots of other forms. 4 of the top-5000 are Carol primes. The largest is currently number 1872 on the list and was found by Emmanuel in May 2007 where it was around number 900. The Prime Pages equivalent of notability is : "An archivable form of prime is one which is the subject of more than one mathematical journal article written by more than one set of authors". No journal articles mention Carol numbers. I subscribe to the mailing list where Emmanuel introduced them in 2002 and mentioned them dozens of times since then. Based on Google searches and my knowledge of list members, I think most people who have ever used the term publicly are from that mailing list, some of them without knowing that Emmanuel invented the name. PrimeHunter (talk) 03:56, 29 January 2009 (UTC)
 * Keep Per Not always having to do the right thing. Let's let one go, once in a while. Charvest (talk) 07:53, 29 January 2009 (UTC)
 * Delete. As I have already indicated in a comment above, the term does not appear anywhere in the published literature.  Moreover, given the fact that OEIS accepts all or nearly all submissions without review, it cannot be used to establish the notability of these primes for the purposes of a Wikipedia article.  That leaves only the Mathworld article.  Perhaps this article could be used as a source to indicate that there is such a sequence of primes in a similarly titled Wikipedia article (Near square primes anybody?). But mention of the sequence of primes under discussion in an obscure place among a list of OEIS entries reprinted in a Mathworld article also does not pass the bar for notability.   siℓℓy rabbit  (  talk  ) 13:53, 29 January 2009 (UTC)
 * Comment It's an idea. We could follow MathWorld and merge Carol number and Kynea number into a new Near-square primes article. Or would that also get shot down ? Gandalf61 (talk) 14:01, 29 January 2009 (UTC)
 * I don't think there would be much of a problem with that. But to be sure we could start with a section on prime searching in largest known prime or another related article. By the way, merge into List of prime numbers could be another option. In practice it would mean moving the references from here to the list, and perhaps adding a footnote that explains where the name comes from. --Hans Adler (talk) 14:18, 29 January 2009 (UTC)
 * Merging to List of prime numbers would be against my suggested point 3 at Talk:List of prime numbers (but it only received one indirectly supporting comment). PrimeHunter (talk) 14:30, 29 January 2009 (UTC)
 * We could use an article for near-square primes, and these two forms would fit naturally there. I'm changing my !vote. CRGreathouse (t | c) 17:12, 29 January 2009 (UTC)


 * Delete – not notable. The MathWorld article is only a redirect page; on the page to which "Carol number" redirects, the term does not even occur. In general MathWorld and OEIS attest only weakly to notability, since they add material quite indiscriminately, freely using neologisms of the inventors of some concept. Before an article named "Near-square primes" is started, we must make sure this is not another MathWorld/Cletus Emmanuel neologism. 88.234.217.196 (talk) 01:39, 30 January 2009 (UTC)
 * Userfy (or weak keep/ delete) with Kynea number. I must admit when I first read the source for the name (2004), I laughed out loud: "Carol G. Kirnon is my best female friend in the whole wide world. She was the first girl to steal my heart when we were in high school. Therefore, since math is my love and she is my love, I named the first set of numbers after her. The second set... is named for the baby girl that had the greatest inpact on my life so far, Kynea R. Griffith" I suspect I am not alone among Wikipedians in that response. However, that reaction shouldn't colour our decision making. This article is better than Kynea number, and the concept, a generalization of the Mersenne prime, has led to new large prime numbers which have been documented in secondary sources, even if they are less than stellar. It may be premature for Wikipedia to have an article on this now, but what there is so far might at least be userfied. Geometry guy 22:48, 31 January 2009 (UTC)
 * Correction: Please strike out your comment as it seems based on a misconception. No new prime numbers have been discovered because of the concept of Carol number.  Emmanuel found that 4 of the 5000 largest, already known primes were of that form.  Hardly the same thing.  As PrimeHunter already explained at length above, one can devise many similar such "concepts", and finding only 5 of that form in a known collection of primes is hardly any evidence it is a useful one.  --C S (talk) 00:34, 1 February 2009 (UTC)
 * I hope you weren't asking me to strike out my entire comment on that basis. I have amended it. Geometry guy 00:50, 1 February 2009 (UTC)
 * No reason to strike it. I'm confident all Carol (and Kynea) primes which are or have been in the top-5000 primes were only searched because Cletus Emmanuel mentioned the form in public (some of the primes were found by himself). All the primes were discovered after 2002 where he first mentioned the form. It was not a case of realizing that already known primes were of this form. The first few Carol primes with less than 18 digits had been previously computed but the top-5000 has required more than 20000 digits since 2002 (more than 100000 today). PrimeHunter (talk) 01:15, 1 February 2009 (UTC)
 * Just to be clear: have there been new primes of the Carol (or Kynea) form discovered since 2004? If so, was the discovery of any of these primes prompted in any way by Cletus Emmanuel's Ansaetze? Geometry guy 01:26, 1 February 2009 (UTC)
 * Yes and yes. The 4 Carol primes currently in the top-5000 were discovered in 2004, 2005, 2006, 2007. Depending on what you call a "form", anybody with a little patience can download a free program, pick one among thousands of simple forms, start the program, sit back, and expect to find a top-5000 prime within a month on a common PC. The computational effort used by GIMPS to find Mersenne primes is around 100000 times larger than what is needed to find the known Carol primes. By the way, Carol primes (2n−1)2−2 = (2n−1−1)×2n+1−1 can be viewed as a special case of an older well-known prime form k×2n−1 with k < 2n, sometimes called Riesel primes after Hans Riesel. They don't have an article such as the more common name Proth prime (k×2n+1), but around half of all current top-5000 primes are Riesel primes. Most people search them with small k values below 232, but it's easy to prove primality for any k < 2n. PrimeHunter (talk) 02:14, 1 February 2009 (UTC)
 * Many thanks for your helpful response. As this endeavour has been going since 2004, is there now a good secondary source for this information? Geometry guy 02:23, 1 February 2009 (UTC)
 * The article references the primary source where the search is coordinated. Apart from that and mail list postings by the searchers, I don't know of any mention of the organized search beyond links to it. Found primes are submitted to http://mathworld.wolfram.com/Near-SquarePrime.html (which itself calls it a "(2n−1)2−2 prime"), A091515, and the Prime Pages which includes a computer generated page for every current and former top-5000 prime. The 4 current top-5000 Carol primes are here: . "Carol prime" is not among the tolerated comments  in the Prime Pages database so it doesn't occur on the pages. Finding a prime below 200000 digits is so simple and common that nobody else usually cares. Most days there are several new of them on http://primes.utm.edu/primes/status.php. PrimeHunter (talk) 03:06, 1 February 2009 (UTC)
 * Thanks. I'm unstriking "new" and striking "weak keep": I don't think the sources are good enough yet, even taken together. Otherwise, I stand by my recommendation, which essentially agrees with your "weak delete". I just want to highlight the possibility that someone could userfy, and also emphasise that if this gets deleted, Kynea number should as well. Geometry guy 21:03, 1 February 2009 (UTC)
 * Thanks to PrimeHunter for his corrections to my earlier remark. I think, however, my remarks as to poor sourcing and lack of evidence of Carol numbers being a "hunting ground" (anymore than many similar formulas) hold.  --C S (talk) 22:40, 2 February 2009 (UTC)


 * Keep as referenced well enough, and that we do not have a printed encyclopedia here; space allows. Bearian (talk) 20:19, 2 February 2009 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.