Wikipedia:Articles for deletion/43,112,609 (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. I hate closing AfD discussions this involved as no consensus but sometimes there is no consensus to be found. There are three positions with some degree of policy and guideline based support: keep, rename, and merge. Based on the spread with which each position is held and that there are legitimate guideline based reasons for each position so we cannot weight that spread away we end with a no consensus. I recommend no renomination, or similar process (e.g. MERGE), for at least three months (and six or months would not be out of order). Barkeep49 (talk) 02:00, 25 June 2020 (UTC)

43,112,609 (number)

 * – ( View AfD View log  Stats )

Is this number important independent of being a Mersenne prime exponent?? Georgia guy (talk) 15:39, 5 June 2020 (UTC)
 * Delete as per my previous PROD and that notability is not inherited. Eumat114 formerly TLOM (Message) 15:40, 5 June 2020 (UTC)
 * Mersenne primes are commonly referred to by their index. SpinningSpark 15:57, 5 June 2020 (UTC)
 * Note: This discussion has been included in the list of Mathematics-related deletion discussions. Eumat114 formerly TLOM  (Message) 15:45, 5 June 2020 (UTC)


 * Delete. There isn't sufficient material to sustain an article on this number, especially once all the trivial stuff about the GIMPS results are removed. –Deacon Vorbis (carbon &bull; videos) 16:56, 5 June 2020 (UTC)
 * Keep. WP:NUMBER suggests that number articles should meet one of three notability criteria,
 * 1. Are there at least three unrelated interesting mathematical properties of this integer?
 * It is a Mersenne prime index (there are ony 51 known such numbers, and only 45 at the time of its discovery)
 * It was the largest such number at the time of its discovery (WP:NTEMP)
 * It is one of a pair of Mersenne prime indexes that are the closest together known (in percentage terms)
 * It is the degree of four of the twelve largest primitive binary trinomials over GF(2)
 * It is the largest of only eight numbers which are both Mersenne prime indexes and Sophie Germain primes
 * 2. Does this number have obvious cultural significance (e.g., as a lucky or unlucky number)?
 * 3. Is it listed in a book such as David Wells's Dictionary of Curious and Interesting Numbers, or Jean-Marie De Koninck's Those Fascinating Numbers, or on Erich Friedman's "What's Special About This Number" webpage?
 * It is listed on page 406 of De Koninck's book. The Penguin Dictionary was last revised in 1997 so is too old to include it (discovered 2008), and Friedman's list is only for numbers below 10,000.
 * It appears in five places in Enciclopedia Matematică a Claselor de Numere Întregi (Mathematical Encyclopedia of Integer Classes).
 * Evidence for meeting GNG include,
 * There is a scholarly paper on the discovery of it and another number.
 * Numerous books published around the time of its discovery name it as the largest such number.
 * SpinningSpark 17:23, 5 June 2020 (UTC)
 * Passing mentions do not demonstrate notability. The (short) paper is just a high-level overview of the search for Mersenne numbers in general and mentions the two most recent (at the time of publication) ones found.  This is insufficient for contributing to meeting WP:GNG. –Deacon Vorbis (carbon &bull; videos) 18:34, 6 June 2020 (UTC)
 * Even putting that aside, the number that's notable here is 2^43,112,609-1, not the number 43,112,609. Eumat114 formerly TLOM (Message) 15:03, 7 June 2020 (UTC)


 * Comment Discovering two Mersenne primes less than 30 days apart from each other is a passingly cute little factoid, and so is a bug causing a prime to go unnoticed for two months &mdash; minor curios of history that might be of interest to those passionate for prime hunting or collaborative computing more generally. They might merit a line or two in the Great Internet Mersenne Prime Search article, but they're not the sort of material that can really support an article by themselves. At the moment, this is seeming to me more of a "selective merge" than either a "keep" or a "delete". XOR&#39;easter (talk) 17:32, 5 June 2020 (UTC)
 * Keep The nomination provides no reason to delete and SpinningSpark provides plenty of reasons not to do so. See also the interesting number paradox. Andrew🐉(talk) 21:05, 5 June 2020 (UTC)
 * Doesn't that 'paradox' imply we should have a Wikipedia page for 0 -> inf? Not sure how the WMF, and their server hard drives, might feel about that. ProcrasinatingReader (talk) 18:53, 7 June 2020 (UTC)
 * Keep: The article has reliable sources. I agree with Andrew that SpinningSpark is making a much better argument for keep than the nominator did for delete. — Toughpigs (talk) 21:21, 5 June 2020 (UTC)
 * Move. The notability of this number very much rests on it being a Mersenne prime index. Nearly all of the properties listed are somewhat linked to its corresponding prime. If anything, this page should be moved to a page like 2^43112609 - 1. The sources provided are all centered around the Mersenne number instead of 43,112,609 itself, and based on WP:INHERITED, the number that should be included is 2^43,112,609-1. Eumat114 formerly TLOM (Message) 03:20, 6 June 2020 (UTC)
 * While that's not such a bad idea, I listed two properties above (namely the degree of a primitive trinomial and a Sophie Germain prime) that are not related to it being an index of a Mersenne prime. SpinningSpark 13:10, 6 June 2020 (UTC)
 * Being a Sophie Germain prime is not so special, as there are 55K such primes below 10 million, compared with 660K primes less than this bound. This means that 8% of the primes satisfy this, which doesn’t make it special. The statement of being a large degree of trinomials can be mentioned in the text of the new destination. Eumat114 formerly TLOM (Message) 13:29, 6 June 2020 (UTC)
 * The bit about primitive trinomials mod 2 related to being a Mersenne number. The source specifically mentions an algorithm that can check this for Mersenne exponents efficiently, so there's no reason to be surprised that they found some for this number.  –Deacon Vorbis (carbon &bull; videos) 18:19, 6 June 2020 (UTC)
 * Since not all Mersenne primes have this property (eg M57885161) it cannot be maintained that the property is synonymous with being a Mersenne prime. Spinning<b style="color:#4840A0">Spark</b> 14:35, 7 June 2020 (UTC)
 * But it is certainly close enough to being a Mersenne prime to be discussed on the page on Mersenne primes itself with 2^43,112,609-1 linking to it. Eumat114 formerly TLOM (Message) 15:01, 7 June 2020 (UTC)
 * And 57885161 is the first Mersenne index without this property, according to the paper, suggesting a very strong linkage between the two. Eumat114 formerly TLOM (Message) 04:33, 15 June 2020 (UTC)
 * Keep per TLOM. ——  Serial # 05:40, 6 June 2020 (UTC)
 * Have you all gone insane? If anyone wants to take note of any historical tidbits about the prime search itself, that can be added at the GIMPS article. That isn't even remotely viable for establishing notability for this number as its own topic.  There are no RSes establishing notability for this.  A one-page short note of a preprint doesn't count; nor do internet forum message boards.  This is absolutely nuts.  –Deacon Vorbis (carbon &bull; videos) 16:42, 6 June 2020 (UTC)
 * see WP:MAD. Andrew🐉(talk) 18:44, 6 June 2020 (UTC)
 * I don't really care if a redirect is left for attribution purposes if someone decides to merge something here, but it sort of misses the ultimate question of "Should there be an article here?". There's not always a clear boundary between AfD and merge/split proposals. –Deacon Vorbis (carbon &bull; videos) 18:49, 6 June 2020 (UTC)
 * is this a pun? Eumat114 formerly TLOM (Message) 10:51, 7 June 2020 (UTC)
 * Very selective merge to Mersenne prime. Brief, non-peer-reviewed preprints and forum posts do not really make a case for independent notability. XOR&#39;easter (talk) 18:56, 7 June 2020 (UTC)
 * Merge into Great Internet Mersenne Prime Search, with an addition to the list at Mersenne prime, per and . ProcrasinatingReader (talk) 19:04, 7 June 2020 (UTC)

<div class="xfd_relist" style="border-top: 1px solid #AAA; border-bottom: 1px solid #AAA; padding: 0px 25px;"> Relisted to generate a more thorough discussion and clearer consensus.
 * Merge into Great Internet Mersenne Prime Search. "2^whatever is a Mersenne prime. Here is some uninteresting trivia about other Mersenne primes to beef up this stublet and make it look like an article. Blah de blah de blah." <b style="color: Maroon;">Reyk</b> <b style="color: Blue;">YO!</b> 11:25, 9 June 2020 (UTC)
 * Delete or Merge to Great Internet Mersenne Prime Search/ alternate Mersenne prime: This is a number that would be mainly of interest to number theorists making stand alone inclusion part of a scientific journal of which Wikipedia is not. There is validity that 2^43,112,609-1 would be more correct. --  Otr500 (talk) 11:57, 10 June 2020 (UTC)

Please add new comments below this notice. Thanks,  Sandstein   07:58, 13 June 2020 (UTC)
 * Keep WP:NUMBER is a well established subject-specific notability guideline and the topic of this article meets that guideline. I am not persuaded by comments here that the guideline has not been met or that WP:NOT applies. Thincat (talk) 09:20, 13 June 2020 (UTC)
 * I'm not sure if you read my argument, but 43,112,609 is not notable whatsoever. What demonstrated was the notability of the corresponding Mersenne prime (which I won't object to keeping but is marginally notable anyways), not 43,112,609. There is no evidence of notability at all regarding 43,112,609 independent of being a Mersenne prime index (WP:INHERITED). Eumat114 formerly TLOM  (Message) 10:44, 13 June 2020 (UTC)
 * I did read your argument and thought it was reasonable. However, I didn't agree with it. Any number discussed on WP needs to be represented in some way, generally by its decimal representation. A number used as an index or exponent is still a number. In this case it is part of (by far the most important part of) the usual representation of the prime. Yes, we could instead have an article titled 2^43,112,609-1 but I don't think that would be so helpful to our readers. Thincat (talk) 11:01, 13 June 2020 (UTC)
 * ...and if we did have such an article, then it would still be justifiable to keep this page as a redirect at least. Until such a page exists, that is a non-argument, but in any event, deletion is not the solution per WP:PRESERVE. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 11:31, 13 June 2020 (UTC)
 * Yes so I advocate for a move and won't object to redirecting it, which is why I didn't put a "without leaving a redirect" after the "Move" – that is, assuming that 2^43,112,609 - 1 is notable. The argument for and against that are both well-reasoned. As for the representation, I can presume someone typing for "43,112,609" would reasonably want to look for the Mersenne prime.
 * Now back to the question: is 2^43,112,609-1 notable? I'm inclined to say no. First, WP:NUMBER doesn't explicitly state that fulfilling one of them guarantees notability. Most of the sources are just short notes and preprints noting the discovery of this number. Whatever is notable about 2^43,112,609-1 can be, or is, reasonably captured in the article on GIMPS or Mersenne prime. De Koninck's book covers every single Mersenne prime with no nite whatsoever on any special properties; that of being a Mersenne prime does not make it good enough for an article.
 * SIDE NOTE: I also noted that the list of numbers there are pretty WP:INDISCRIMINATE: it includes some virtually random number with some meaningless properties; for instance, p. 344 of the book lists 3,504,597,120 as "the 13th number n such that ϕ(n)+σ(n)=4n"; I don't see how notable that makes this otherwise random number. Eumat114 formerly TLOM (Message) 08:50, 14 June 2020 (UTC)
 * Keep - As per comments above this number appears to meet the requirements to be notable under WP:NUMBER and can be well references as an individual article.Tracland (talk) 20:16, 13 June 2020 (UTC)
 * Did you even read them? There's nothing interesting about this number whatsoever. –Deacon Vorbis (carbon &bull; videos) 20:20, 13 June 2020 (UTC)
 * WP:INTERESTING is also something worth reading. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 00:12, 14 June 2020 (UTC)
 * The arguments presented there are probably invalid when WP:NUMBER literally says "unrelated interesting properties". And WP:1729 is a pretty objective way to measure interesting-ness. Eumat114 formerly TLOM (Message) 08:57, 14 June 2020 (UTC)
 * Objective != notable (or even sensible), and I humbly suggest that any formula involving Erdos number and OEIS page number is the very epitome of irrelevant for our purposes. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 12:03, 14 June 2020 (UTC)
 * It is patent nonsense when taken literally. But it provides a good standard for guesstimating the "interestingness" of a number; for example, being a Harshad number != interesting while being a small Carmichael number = interesting. Now to justify notability, please provide 2 interesting properties of either 43,112,609 or 2^43,112,609-1 independent of being a Mersenne prime/the largest prime number. (I count that as one property.) Eumat114 formerly TLOM (Message) 04:31, 15 June 2020 (UTC)
 * I would argue that the trinomial property is independent of the Mersenne prime property. Not all primitive trinomials over GF(2) have a degree equal to a Mersenne prime index, and not all Mersenne prime indices are degrees of a primitive trinomial over GF(2).  The sets intersect, but neither is a subset of the other.  They only appear to be related properties because the trinomials are particularly easy to find in relation to a Mersenne prime so that is where research is concentrated.  To argue that they are related would be a bit like arguing that the deficient numbers are related to the even numbers because some deficient numbers are even. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 10:47, 15 June 2020 (UTC)
 * But then we have a problem; there are so many of these that being an exponent is no longer special. For instance, this site lists a good number of primitive trinomials, of which quite a few don't have Mersenne index degree:
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * 1
 * With this analysis in hand, as 16 out of 25 of them not having Mersenne prime index (the bolded ones), it is not hard to see why being a trinomial degree hardly carries interest or notability, and especially that the 4 out of 12 trinomials are discussed together. This can be discussed in the page on Mersenne prime, but not enough to warrant unique articles. Eumat114 formerly TLOM (Message) 12:35, 15 June 2020 (UTC)
 * the claim is that these are some of the largest primitive trinomials GF2, not any old primitive trinomials. The largest degree on that list is 32.  Our number is well over a million times more interesting than that on that basis (43,112,609÷32=1,347,269). <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 14:54, 15 June 2020 (UTC)
 * Well -- I guess we can agree that the property of being a prime is much more well-researched and well-known than having an obscure property such as the degree of a primitive trinomial. The level of interest generated by 43,112,609 as a Mersenne prime. According to the standard laid out in WP:1729, no mathematician has really written a paper on 43,112,609 as "one of the largest trinomials with this property" independent of others. In contrast, a lot have written about 43,112,609 as a Mersenne index. Eumat114 formerly TLOM (Message) 01:52, 16 June 2020 (UTC)
 * I mean, being the largest of an obscure class of numbers is radically different from being the largest of a well-known class of numbers (i.e. primes). Plus, many of the sources mentioning 43,112,609 and primitive trinomials also mention its Mersenne index property, so it would make great sense to merge into the article on primitive trinomials or Mersenne prime -- much more sense than leaving each and every index as a standalone article. cf. WP:INDISCRIMINATE Eumat114 formerly TLOM (Message) 02:00, 16 June 2020 (UTC)
 * Yes, a mathematician has written a paper on the trinomial property; the "Twelve new primitive binary trinomials" article I added to the page as a reference. So you are going to dismiss Sophie Germain prime as being too common, and dismiss the degree of a binary trinomial as obscure and esoteric? <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 02:43, 16 June 2020 (UTC)
 * No, not exactly, but that "the degree of 4 of the 12 largest known binary trinomials" (not even the largest) as rather obscure. We only have ~100 articles on individual numbers greater than 300. In terms of fame and popularity, 2^43,112,609-1 just doesn't have enough to be included. 2^43112609 - 1 is currently a redirect to Mersenne prime. Eumat114 formerly TLOM (Message) 03:29, 16 June 2020 (UTC)
 * You can say that 43,112,609 is an odd number, 1 less than a multiple of 90, and is 1 more than a multiple of 8, and you can list out a million more properties of that number. Do these make such a number notable? No, or Wikipedia will become a WP:INDISCRIMINATE collection of info. To list out every number with 3 meh properties is not the purpose of Wikipedia. The "paper" you listed out was probably more of a non-peer-reviewed "press release", and falls short of establishing notability. A close read of the source states that it is basically a "hey, I found a bunch of numbers, and here is how I found them" notice and not really a scholarly article. Eumat114 formerly TLOM (Message) 02:52, 18 June 2020 (UTC)
 * Please don't try to smear the source with it's only a "non-peer reviewed press release". Brent and Zimmermann are not nobodies with a fringe theory.  They can easily be shown to be recognised experts who have previously published in reliable sources in the relevant field and thus meet the requirements of WP:SPS.  In fact, they previously published this and their table 3 in that paper shows that this number was the degree of the four largest known GF(2) trinomials at the time of publication.  Your examples are unconvincing.  I don't know what the largest odd number ever published in a math paper is, but I can easily find a larger one by adding two to it. Likewise, I can add 90 to your second example, or eight to your third.  By contrast, these trinomials are enormously difficult to find requiring massive computing resources.  There is no comparison at all. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 13:33, 18 June 2020 (UTC)
 * I can let this property go as establishing significance, even though I'm still in favour of merging the contents into Mersenne prime as one of its applications. I'm not dismissing Richard P. Brent and Paul Zimmerman as nobodies. But wouldn't it make more sense to convey the information here in the article Mersenne prime, noting their discoveries and stating this application?
 * Plus, is there a third property of either number that makes it notable? Eumat114 formerly TLOM (Message) 14:15, 18 June 2020 (UTC)
 * Let's sort out where we're heading: if we were to keep either one of "43,112,609" or "243,112,609-1", which one are you edging for? Eumat114 formerly TLOM (Message) 00:51, 19 June 2020 (UTC)
 * Delete. The mere presence of reliable sources (which appear to have trivial mentions only) and singular interesting property as a Mersenne prime exponent do not make this number notable enough for a standalone article.Per WP:NUMBER:
 * 1. Are there at least three unrelated interesting mathematical properties of this integer?
 * The keyword here is unrelated. From the looks of the article and sources, a pretty clear no. Everything described rests on it being the exponent for M43,112,609, and notability is not inherited. Not that it would matter, because that number is only notable for being a Mersenne prime (one property) and it's not even the largest known. I don't see what else is so unique, interesting, or not obscure that would fulfill this criterion. Based on what I'm reading above, such reasoning could lead to almost any number (even arbitrarily large ones) being deemed notable and having an article written, and Wikipedia is not a directory of indiscriminate number trivia. Is 6,700,417 notable for being a factor of F5 and once-upon-a-time the largest known prime? Or 33,550,336 for being the first perfect number not known to the ancients and the first with multiple digits that sum to a perfect number (28)? The list goes on and on, even more easily with less obvious mathematical properties such as these trinomials; to be frank, I'm not entirely understanding some of the keep !votes above.
 * 2. Does this number have obvious cultural significance (e.g., as a lucky or unlucky number)?
 * No. Anything not obvious pertaining to its discovery is already adequately summarized at GIMPS or Largest known prime number.
 * 3. Is it listed in a book such as David Wells's Dictionary of Curious and Interesting Numbers, or Jean-Marie De Koninck's Those Fascinating Numbers, or on Erich Friedman's "What's Special About This Number" webpage?
 * I'm open to being proven wrong, but I think it highly unlikely that it would receive a nontrivial mention (i.e. outside a list of Mersenne exponents) or any mention at all, as there are millions of other numbers with "interesting" or "fascinating" properties. The line needs to be drawn somewhere, and I'm pretty sure this number does not uniquely cross it for a number of its size and nature. ComplexRational (talk) 20:53, 18 June 2020 (UTC)
 * Changing to move to 2^43112609 - 1 over redirect, delete 43,112,609 (number) as a redirect, and selective merge from there into Great Internet Mersenne Prime Search. See my comments below. ComplexRational (talk) 02:12, 24 June 2020 (UTC)
 * 3. Is it listed in a book such as David Wells's Dictionary of Curious and Interesting Numbers, or Jean-Marie De Koninck's Those Fascinating Numbers, or on Erich Friedman's "What's Special About This Number" webpage?
 * I'm open to being proven wrong, but I think it highly unlikely that it would receive a nontrivial mention (i.e. outside a list of Mersenne exponents) or any mention at all, as there are millions of other numbers with "interesting" or "fascinating" properties. The line needs to be drawn somewhere, and I'm pretty sure this number does not uniquely cross it for a number of its size and nature. ComplexRational (talk) 20:53, 18 June 2020 (UTC)
 * Changing to move to 2^43112609 - 1 over redirect, delete 43,112,609 (number) as a redirect, and selective merge from there into Great Internet Mersenne Prime Search. See my comments below. ComplexRational (talk) 02:12, 24 June 2020 (UTC)


 * Weak Keep: Considering all the points that stated and the historical as well as cultural significance that this number has based on the fact that it is ONE of the only 51 such numbers, it should be kept without any doubt. Wikipedians who are a part of Wikiproject Mathematics should be called here because they won't view it as "just a number", unlike the rest here. If 800 can have its own article regardless of the fact that it has no cultural significance whatsoever, then this should obviously have its own as well. Clearly passes WP:SIGCOV as well. Regards <b style="color:NavyBlue">Pesticide 1110 </b> <i style="color:Teal">Lets wrestle!</i> 08:17, 19 June 2020 (UTC)
 * , I know, but Category:Integers show only 393 numbers, and hence only about 100 numbers over 300 are independently notable (not for a range) and just 11 over 10K. If it were the number 2^43112609-1 I can argue about that. But being a mere exponent of a possibly notable number carries no significance whatsoever. That is why I advocate for at the very least a move, presumably to a page named 2^43112609 - 1. Even then the level of notability is dubious, but at least greater than 43112609. Eumat114 (Message) 09:19, 19 June 2020 (UTC)
 * I'm getting very mixed feelings about the whole issue. The is one of the more complicated afds. It took me more than 45 mins to read the whole discussion and even after that i'm very much confused about the whole situation. Both the sides have got brilliant points but a decisive factor is still missing somehow. Can you help? Regards <b style="color:NavyBlue">Pesticide 1110 </b> <i style="color:Teal">Lets wrestle!</i> 09:29, 19 June 2020 (UTC)
 * Yes, I'm very much with you on this (I !voted keep). It seems to me both sides are giving utterly good faith subjective opinions. I can understand why some people do not think the number is (sufficiently) interesting. What I find very puzzling is that they also by implication feel that in future other people shouldn't be allowed to read the article. I can't come close to understanding that.Thincat (talk) 10:10, 19 June 2020 (UTC)
 * I just feel that much of the stuff, if keepable, have been, or can be, adequately summarized in existing Wikipedia articles. The fact that it is a Mersenne index is established in Mersenne prime; the "remarkable" trivia on similarly-timed discoveries may or may not be included in Mersenne prime or GIMPS. That of primitive trinomials can potentially be listed as an application to Mersenne primes. That of being a Sophie Germain and Gaussian prime (which BTW is practically trivia) can be omitted. I shall write a draft describing how it might look like if it were to be merged, at Draft:Mersenne prime (modification). Eumat114 (Message) 11:17, 19 June 2020 (UTC)
 * Yes, I think that shoving trivia and near-trivia together to make something resembling an article does a disservice to the subject of Mersenne primes. It's not that I feel other people shouldn't be allowed to read the article; I just don't find that the article can live up to the standards that Wikipedia should try to embody, and its existence doesn't help anyone learn about mathematics. XOR&#39;easter (talk) 21:54, 19 June 2020 (UTC)
 * I agree with XOR'easter. We shouldn't try to polish this up if it's still not notable—no amount of editing changes a subject's notability and keeping an article like this would raise serious questions and considerations about out notability standards. And one could argue that many (subjectively) interesting articles get deleted at AfD everyday because interestingness and aesthetics do not compensate for a lack of notability... nobody comments about people not being able (or technically allowed) to read those anymore. ComplexRational (talk) 13:18, 20 June 2020 (UTC)
 * Plus, as I said above whatever is useful in the article has been, or can be, captured in the article Mersenne prime. Eumat114 (Message) 13:28, 20 June 2020 (UTC)
 * While I appreciate the ping, I am not particularly familiar with math-related notability, and as this is a very borderline case I'm going to refrain from !voting. All the best, Eddie891 Talk Work 12:16, 19 June 2020 (UTC)


 * Merge whatever's needed to Great Internet Mersenne Prime Search. The sources in question only cover the number in context of the prime search, thus the number should be covered proportionately within the prime search's article. There isn't enough material to source a full article on the number itself. I doubt the redirect's helpfulness, but all in all, this is a fine alternative to deletion. (not watching, please )  czar  18:27, 20 June 2020 (UTC)
 * I !voted delete in part because the redirect won't be very helpful. Even if it becomes an R with history, it will inevitably find its way to RfD because not even four-digit numbers have redirects, and having redirects for numbers of comparable notability (for lack of a better word) to 43,112,609 would not make sense, be difficult to maintain, and perhaps double the number of existing redirects in all of WP. Since most of the content is not unique to this article, is there a way to either only add what may be missing or otherwise find some other way of attributing? I would say "merge and delete", as this is written to convey greater notability than there is and the redirect may be problematic, but this could run into attribution issues. ComplexRational (talk) 14:17, 23 June 2020 (UTC)
 * , I'm not aware of any precedent at RfD that would lead to its deletion. It remains a valid search term (someone who is looking for this number is not looking for anything else and could likely lose the disambiguation) so like I said, I think it's more about this being a valid alternative to deletion and preserving sourced content. And yes, once the content is merged, the page history will need to be kept for attribution reasons. (not watching, please )  czar  01:12, 24 June 2020 (UTC)
 * Sorry for not linking them earlier. The most recent RfDs that I am aware of, pertaining to four digit numbers, are from September and December 2018; the latter refers to the former as a precedent. As an alternative to deletion, it could make sense, but what to do with the redirect is still debatable. ComplexRational (talk) 01:40, 24 June 2020 (UTC)
 * Merge into Great Internet Mersenne Prime Search. I was going to close this discussion to that effect, but I can see it being argued that the discussion is on the edge, so I will instead !vote to move it towards a clearer resolution. With respect to WP:NUMBER arguments, I would suggest that you could pick literally any number—any number at all, be it 34,985,397,239,587,952 or 89,572,678,257,853,636 or 594,869,379,486,798,778—and if you investigated it deeply enough you would find three properties that would pique the interest of mathematicians. Perhaps one of them would turn out to be the sum of seven consecutive cubes, or is the exact reverse order of some weird prime, or is a string of digits of pi starting at a digit representing the sum of seven consecutive cubes. The point is, this number is not particularly more remarkable than any of billions of other numbers for which some interesting properties can be identified. However, as long as there is something to be said about it, it seems harmless enough to merge it into the most relevant article for the characteristic that makes it interesting. I would merge it pretty much as is, in its entirety. BD2412  T 05:14, 22 June 2020 (UTC)
 * Should we leave a redirect, for this number and other Mersenne prime indices? Eumat114 (Message) 10:52, 22 June 2020 (UTC)
 * I would assume that a merge includes a resulting redirect. Also, following from my rationale here, if a number is theoretically "interesting" for several reasons, I would presume that the merge target and resulting redirect target would be the thing for which it is most interesting. BD2412  T 19:18, 22 June 2020 (UTC)
 * If you don't find this number interesting, I wonder what you make of, for instance, 83 (number), which gets past the WP:NUMBER criteria purely on a "completeness" argument. Mathematicians have paid a lot more attention to this number than they ever did to 83. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 20:23, 22 June 2020 (UTC)
 * 83 is (according to that article) also the atomic number of Bismuth, and the age at which Jews are permitted to have a second bar mitzvah. What is 43,112,609 the atomic number of? What do Jews do when they reach the age of 43,112,609? Generally speaking, numbers in the two or three digits will have some other human connection that makes them interesting not only mathematically (although some mathematical points of interest are also identified for 83). Also, to the extent that anyone will ever actually look up 43,112,609 in Wikipedia, merging as proposed means they will find all of the mathematically interesting information about it in the context of that broader topic. BD2412  T 21:29, 22 June 2020 (UTC)
 * The mathematical facts about this number are way more trivial than for 43112609. There would be no question that people here would bash it relentlessly if it wasn't a low number.  Being the sum of three consecutive primes is not all that spectacular.  A list of such numbers  is easily generated from a list of primes.  Even being a prime that is the sum of three consecutive primes  is not that special.  And note that that is the intersection of two properties, which I have been told repeatedly here does not count as a separate interesting fact.  It is not the smallest such number, nor anywhere near the largest known.  There are infinitely many of them and way more are known than the known Mersenne prime indices.  I note also that one of its other "interesting" properties is being a Sophie Germain prime, which I have also been told here is not interesting enough to count.  The non-mathematical social facts are even more trivial.  Being an atomic number is not special either, since all numbers are atomic numbers up to the highest so far discovered element.  I'm pretty convinced that there is rather less written about 83 as a number than has been written about 43112609. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 23:04, 22 June 2020 (UTC)


 * From what I know, 43112609 is expected to be the atomic number of Quadtriununbihexnilennium, or as we call it, Unobtanium. If you can synthesize it, by all means please do so. Jews, like everyone else, would have become a fossil by age 43,112,609. The "completeness" argument makes much sense -- what would one think of Wikipedia if the number 83 is not covered? Anything at most 2 digits long are bound to have some culturally significant facts with it. Doesn't apply to 43,112,609, especially since its destination is what the reader expects. Eumat114 (Message) 09:44, 23 June 2020 (UTC)


 * Since I haven't made either an atomic number or culturally significant argument for 43112609 your comments are meaningless, amd by the way, see Wandering Jew in relation to your citation needed. My point actually was that none of these properties establishes notability of 83 under GNG; it relies entirely on WP:NUMBER.  The completeness argument actually flies directly in the face GNG, as NUMBER itself readily admits.  And on that I'll just point out that NUMBER allows 101 articles under that clause whereas the number of currently known Mersenne prime indices is only half that at 51. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 10:46, 23 June 2020 (UTC)
 * According to WP:NUMBER, for the sake of completeness, however, it is accepted that every integer between −1 and 101 has its own article even if it is not as interesting as the others. This avoids having, say, a gap for 38. This echoes with my view on why 83 (number) exists even if it is less notable than 43,112,609. Yeah, my above comment, esp. pertaining to Unobtanium, can be taken as a joke to lighten up the mood. Eumat114 (Message) 11:20, 23 June 2020 (UTC)
 * In all seriousness, though, there was an agreement to keep those number articles as it is and no consensus (yet) to keep each number with one single spectacular property. You can obtain it at an RFC; I won't stop you. Beware –&#32;consensus might. Eumat114 (Message) 12:13, 23 June 2020 (UTC)
 * Keep. It has been proven by induction that all natural numbers are interesting. Stifle (talk) 10:54, 23 June 2020 (UTC)
 * [ proof needed] Eumat114 (Message) 11:07, 23 June 2020 (UTC)
 * I think Interesting number paradox is being referred to here, for which a "proof" in a reliable source can be found here. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 12:34, 23 June 2020 (UTC)
 * Yes, any number can be called interesting for being the first "non-interesting" number, which in turn makes it interesting. But we're not creating number articles (or even redirects) ad infinitum; the notability guidelines exist for this reason. Is this !vote serious? ComplexRational (talk) 14:17, 23 June 2020 (UTC)
 * Hence my humorous maintenance tag. Eumat114 (Message) 14:46, 23 June 2020 (UTC)
 * Should it be made clear that this, like the collapsed section above, was a joke? ComplexRational (talk) 16:09, 23 June 2020 (UTC)
 * The rationale is clearly a joke. The "keep" opinion may or may not be, so should not be collapsed unless the OP chooses to so do. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 21:03, 23 June 2020 (UTC)
 * Keep: Notable number of sweet beauty and per Spinningspark.Djm-leighpark (talk) 15:35, 23 June 2020 (UTC)
 * Gonna need a relist. Eumat114 (Message) 15:38, 23 June 2020 (UTC)
 * Yes, definitely a relist, discussion is still very active. And what exactly constitutes "sweet beauty", if I may ask? ComplexRational (talk) 16:09, 23 June 2020 (UTC)
 * No, a relist is not needed, except for the purpose of giving Eumat114 more opportunity to try and WP:BADGER everyone into submission. No new arguments have been offered (joke contributions aside), it's just the same old stuff being rehashed.  The last new source offered was by me on the 20th and I don't believe that any new policy or guideline rationales have been offered for over a week. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 16:27, 23 June 2020 (UTC)
 * Comment. No relist needed – close this now as a textbook case of no consensus.  Strong points made on both sides (slight bias to weak keep), but no clear winner.  Ultimately, we are WP:NOTPAPER, and this number, after this epic AfD, seems to have won the right to fight for another day.  No harm will come to WP as a result:) Britishfinance (talk) 20:06, 23 June 2020 (UTC)
 * There is certainly not no consensus here, should an analysis of the arguments be made. Discussion is still active; a resolution or, failing that, a relist is warranted. Some votes are just humour, like Stifle's.ProcrastinatingReader (talk) 01:38, 24 June 2020 (UTC)
 * Even this deep into the AfD (and reinforced by subsequent comments below), I just don’t see signs of any consensus emerging. Britishfinance (talk) 09:42, 24 June 2020 (UTC)
 * Comment:
 * This AFD is overdue for 4 days already, for a total of 18 days. Any further relist might come into contradiction with WP:RELIST: in general, debates should not be relisted more than twice. This discussion is getting stagnant, but I believe the core idea is worthy of an RFC at WikiProject Mathematics if a revision to WP:NUMBER is needed;
 * The consensus has swayed wildly from a keep to a merge. It seems unlikely that we will ever achieve consensus in a short period of time; a relist seems to be pointless as per the above, and a no consensus keep is warranted (after all, it's no harm);
 * It appears that nobody has ever bothered to answer the question I set out quite a while ago: Which one should we keep, 43,112,609 with 2 not-so-interesting properties and 2^43112609 - 1 with 1 very interesting property and is significant? Most of the argument are centered on it being an interesting number, which I presume is pertaining to 2^43112609 - 1;
 * I take allegations of WP:BADGERing pretty seriously. The thing is, yep, I admit to it (well, kind of) and as per that page, I'm gonna step back. But I would want an answer to the above age-old question, in particular for a future RFC on WP:NUMBER. I welcome any opinions to improve my discussion participating, especially since WP:Editor review is no longer present and I'm not so experienced.
 * Thank you. Eumat114 (Message) 01:47, 24 June 2020 (UTC)
 * Of the two, I'd rather keep 2^43112609 - 1 as a redirect, since that is the number with the more interesting property and that was formerly the largest known prime. So as an alternative to deletion, I would now recommend:
 * Move over redirect to 2^43112609 - 1 (an admin needs to do this, but it was never a content page)—after all, it seems the focus is really this number,
 * Delete the resulting redirect at 43,112,609 (number) per my comments above and the old RfDs (attribution would not be a problem at this point, and with another redirect in place, this would be an otherwise insignificant 8-digit number), and
 * Merge the new content at 2^43112609 - 1 to Great Internet Mersenne Prime Search or another suitable target (this redirect would make more sense), per most of the merge !votes above.
 * I'm striking my delete !vote in favor of these three steps. I feel this addresses everyone's concerns about notability, the resultant redirect, and attribution of the current article's sourced content. Thoughts? ComplexRational (talk) 02:12, 24 June 2020 (UTC)
 * You asked me this question directly earlier. My apologies for not answering, but I felt discussing the title was unnecessarily complicating an already difficult AfD.  The primary role of the AfD is to decide whether to keep the page.  Naming could have been discussed later, but as we are having the discussion, here is my opinion.  I favour moving to 43112609.  That is, without the separators or disambiguator.  Firstly, because "2^43112609 - 1" is a poor search term.  A user looking explicitly for the Mersenne number is much more likely to type M43112609 which could be a redirect.  "2^43112609 - 1" is not proper maths notation; it is how expressions are represented in some coding languages and an informal way of typing in text only files.  We shouldn't have such ghastliness in a Wikipedia title.  Secondly, 43112609 has some properties other than being a Mersenne index – the trinomial property and some other minor stuff which would be off topic in a Mersenne number article. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 08:38, 24 June 2020 (UTC)
 * I can’t see the purpose in replacing “43112609” with "2^43112609 - 1", which is a more obscure search term? Thanks. Britishfinance (talk) 09:42, 24 June 2020 (UTC)
 * M43112609 would also be a suitable place to relocate the history. I advocate a replacement because the notability of 43,112,609 is inherited from the Mersenne prime, and not notable in itself. It may be more obscure, but it (or M43112609) is more correct than 43,112,609 given the content and the nature of the "interesting" property. ComplexRational (talk) 15:44, 24 June 2020 (UTC)


 * Keep per arguments by . Also, if something was important and notable, it should have an article. Deleting this might create a terrible precedent that would justify the wholesale deletion of mathematics and sciences articles. I am anxious that we are becoming pop-culture-pedia, not Wikipedia. Bearian (talk) 15:07, 24 June 2020 (UTC)
 * No, "importance" has no bearing on whether or not something should have an article, only its notability. And this isn't notable.  There is nothing noteworthy about this number aside from it being a Mersenne prime exponent, and that's not enough to sustain an article.  It merits an entry where we keep a list of the known Mersenne primes; that's it.  Deleting this sets no precedent for deleting math and science articles; that's a nonsense argument.  The historical anecdote about the GIMPS search has nothing to do with this number, and has everything to do with about GIMPS itself.  This number isn't notable. –Deacon Vorbis (carbon &bull; videos) 20:57, 24 June 2020 (UTC)
 * Keep: while I don't find this the most exciting article, the delete case is technical rather than showing evidence of harm, the content is maintainable and verifiable, and it generally seems natural to put content relating to particular numbers under those numbers. Unless and until we have an RfC establishing a better way of treating this kind of material, I think it's best to leave things as they are. &mdash; Charles Stewart (talk) 20:13, 24 June 2020 (UTC)
 * What part of "this isn't notable" is technical? Because this isn't notable.  What part of the WP:deletion policy requires any evidence of harm to be shown, rather than a simple lack of notability? This doesn't require an RfC.  It's simply fails WP:GNG by a wide margin.  And if you really want harm, try the Pandora's box of millions of trivial number articles keeping this opens. –Deacon Vorbis (carbon &bull; videos) 20:57, 24 June 2020 (UTC)
 * I wouldn't object to an RfC if necessary, especially if there are questions as to this would set a precedent (regardless of the outcome). However, I'm still not at all convinced it satisfies GNG. My only reason to not delete is content attribution if a merge is performed (which seems sensible if done correctly); keeping indeed opens up endless possibilities as I outlined above.
 * And as I understand it, certain speedy deletion criteria already exist for the purpose of removing harmful content. Many articles that are not "harmful" go through AfD every day in complete accordance with the deletion policy, and delete/keep !votes are based around policies such as GNG and NOT; harm is not even a factor because CSDs take care of the most obviously harmful cases. ComplexRational (talk) 21:12, 24 June 2020 (UTC)
 * Yeah, I should have been clearer about keeping the article history for attribution purposes rather than outright deletion, but my basic point remains the same. –Deacon Vorbis (carbon &bull; videos) 21:46, 24 June 2020 (UTC)
 * I don't want to live on this planet anymore. –Deacon Vorbis (carbon &bull; videos) 20:57, 24 June 2020 (UTC)


 * The above discussion is preserved as an archive of the debate. <b style="color:red">Please do not modify it.</b> 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.