Wikipedia talk:WikiProject Numbers/Archive 7

Palindromes
I've notice that many of the number articles list the bases in which they are palendromes. Many of of those are "trivial" palendromes; if $$ n = a \times (b+1)$$, with a < b, then $$n = aa_b$$ (If a = b+1, then $$n = 121_b$$ or, if b = 2, then $$n=9=1001_2$$, but this may be getting more complicated then appropriate for the definition of a "trivial" palendrome.

In other words, if n = c &times; d is composite, with c < d-1 (or c = d), n is a palendrome in base d&minus;1. I propose that if we list the bases in which a number is palendromic, we should omit those which are one less than a factor t of n which is greater than $$\sqrt{n+\tfrac 1 4} + \tfrac 1 2$$. — Arthur Rubin (talk) 23:20, 17 December 2018 (UTC)
 * Simpler idea (maybe equivalent?): we only list palindromes of four or more digits. —David Eppstein (talk) 23:41, 17 December 2018 (UTC)
 * Equivalent would be palindromes of three or more digits. I'm not sure a three-digit palindrome is "trivial".  — Arthur Rubin  (talk) 23:52, 17 December 2018 (UTC)
 * This applying to many numbers and number entries, I would like to get consensus somewhere before starting to implement it.... — Arthur Rubin (talk) 21:09, 6 June 2019 (UTC)

Powers, and more
I've noticed (because Eighth power was recently created) that we have a series of power articles,
 * Square · Cube · Fourth power · Fifth power · Sixth power · Seventh power · Eighth power

and I was wondering if we should add a simple template in the "See also" section to include this as a template, or possibly change Classes of natural numbers to allow the sections to be individually collapsible. The former could be done fairly easily, but the latter requires some discussion, as it require re-expanding dozens of articles, and might not be done automatically. I'm not sure replacing Navbox with Navbox with collapsible groups won't break something. — Arthur Rubin (talk) 21:20, 6 June 2019 (UTC)
 * I'm not at all convinced that all of these higher powers have sufficient independent notability for their own separate articles. And I'm somewhat suspicious that the article creator is a returning known sockpuppet. —David Eppstein (talk) 21:35, 6 June 2019 (UTC)
 * FYI moved the new article to draftspace as Draft:Eighth power. —David Eppstein (talk) 06:05, 7 June 2019 (UTC)


 * Greetings. I moved Eighth power to Draft:Eighth power as no sources were provided. Just an additional note, any articles related to mathematics / technical with half the page full of equation/proofs/etc is hard to us, the NPP/AfC reviewers, to review the articles as it is challenging for us to understand the content, it would be good if we have editors who are experts with good standing in Wikipedia in that fields to help up.Cheers. CASSIOPEIA(talk) 06:37, 7 June 2019 (UTC)

RM on 911
not me but somebody else. © Tb hotch ™ (en-2.5). 19:45, 20 June 2019 (UTC)

Number redirects
Nearly all numbers from 300 to 999 with no article are non-section redirects to one of 300 (number), 400 (number), 500 (number), 600 (number), 700 (number), 800 (number), 900 (number). For example, 362 (number) redirects to 300 (number) and not 300 (number) or 300 (number). I suggest all number redirects should go to a section about the number if it exists, otherwise a section about the decade like 900 (number). This always exists for 3-digit numbers. There is often very little information about the number but that's still better than the start of a long list where 99% is about other numbers. All 3-digit numbers have at least the prime factorization, or say it's prime. PrimeHunter (talk) 00:42, 1 April 2019 (UTC)
 * Support. I did this for the 4-digit redirects such as 1111 (number) about a year ago. Certes (talk) 01:12, 1 April 2019 (UTC)
 * I've done 3xx (plus a few stray 2xx that were wrong) and will continue in a few days if no one shouts at me. Certes (talk) 21:00, 20 June 2019 (UTC)
 * ✅ Certes (talk) 15:08, 24 June 2019 (UTC)

List of numbers
See Talk:List of numbers; I don't think the list is very well watched (certainly not by me), and I'm proposing a reversion of a section. I think the format might be of interest to the project. — Arthur Rubin (talk) 02:05, 1 July 2019 (UTC)

3 digit number move discussions
See User talk:Crouch, Swale/Year DAB for a move discussion involving numbers 101 to 125, note that after those have been processed numbers 126 to 150, then 151 to 175, then 176 to 200, then finally any other. Any that are objected at that discussion page or at RMT will be subject to a normal RM.  Crouch, Swale  ( talk ) 20:26, 13 December 2019 (UTC)

Centered pentachoric number
See Talk:Centered pentachoric number; I'd like help determining if this unsourced out-of-the-way article belongs in Wikipedia or in figurate numbers, where I ran across it. — Arthur Rubin (talk) 20:58, 21 December 2019 (UTC)

Overlinking by IP user
An enthusiastic IP editor has made a number of edits which are being reverted, specifically adding links to power of two etc. to articles such as 100,000. Is it appropriate? (copied from previous discussion) tLoM (The Lord of Math) (Message) 16:23, 13 March 2020 (UTC)
 * An enthusiastic logged-in editor has made a duplicate of the discussion immediately above. Is it appropriate? —David Eppstein (talk) 20:39, 20 March 2020 (UTC)
 * , the reason I brought this thing here is because of 's suggestion to bring the overlinking down here, as seen by this edit. Somehow Dhrm77 replied about the overlinking (of all these Power of 2) by those IPs) at the upper section. Let me rename the upper section now, but thanks. TLOM (The Lord of Math) (Message) 03:31, 21 March 2020 (UTC)

Notability of numbers added by IP
An enthusiastic IP editor has made a number of edits which are being reverted, such as converting 2048 (number) and 4096 (number)‎‎ from redirects to articles, and adding links to power of two etc. to articles such as 100,000. (Covered by next section) About 20 articles are affected. Can we agree whether these changes are a good idea? Certes (talk) 13:47, 13 March 2020 (UTC)
 * I've invited the IP editor to this discussion. Certes (talk) 13:59, 13 March 2020 (UTC)
 * Comment the two articles which have come to my attention 2048 (number) and 4096 (number)‎‎ appear to fail WP:NUMBER. Unless the IP user can provide sources as to why these numbers are in fact notable enough to require a standalone article then the redirects should stand. The IP should be warned that they may be blocked if they continue reverting these redirects. Polyamorph (talk) 14:06, 13 March 2020 (UTC)
 * I'd like to take part in this discussion, but it's 11:30pm in my time zone on a Friday night, so you might expect a longer response. Cheers, tLoM (The Lord of Math) (Message) 15:30, 13 March 2020 (UTC)
 * Ok, first we are already talking about 2 different things here:
 * First is the addition of power of two and power of three by an IP user. I reverted the first one I saw, because it seemed redundant with what came next.. but since there are articles about powers of 2 and 3, then why not link to those..
 * second is the standalone articles for 2048 and 4096. My feeling is that these numbers are used all the time in programming and analog to digital conversion, and I would lean to be in favor of keeping these in a standalone article.
 * But perhaps we should start by spliting this conversation into these 2 subjects. Dhrm77 (talk) 16:20, 13 March 2020 (UTC)
 * Courtesy IP address: 176.88.102.71
 * Contents of some of the pages that were created by that user:

4096 is the natural number following 4095 and preceding 4097. 4096 is a power of two: 2$12$ (2 to the twelfth power).


 * In this state, this page definitely fails WP:NUMBER. But I think that some of these pages do have (a slight) hope of turning into articles. I might try to find these interesting properties. tLoM (The Lord of Math) (Message) 16:20, 13 March 2020 (UTC)
 * I agree with . So let me split itso the upper part is about the notability of numbers while the lower part is about linking the power of two's. tLoM (The Lord of Math) (Message) 16:23, 13 March 2020 (UTC)
 * Perhaps as a compromise, we could place of link to power of two on the power itself, for example :
 * 131,072 – 217
 * Dhrm77 (talk) 20:29, 20 March 2020 (UTC)
 * I agree. Why not? It achieves the desired effect while avoiding redundancy. TLOM (The Lord of Math) (Message) 03:32, 21 March 2020 (UTC)
 * I don't think it's a good idea to wikilink formulas, or parts of formulas, especially when the link is not to that exact formula, but rather to part of it (in this case, the 2^ part but not the exponent). See e.g. MOS:EGG: why should a reader expect the text "211" to go to that article rather than an article about exponentiation more generally, or 11'th powers, or whatever? I'd rather see it the way 2048 and 4096 are now linked: "power of two 211", so that the target of the link is clear even without clicking or hovering. So I think the IP's edits e.g. to add this text to 100,000 are harmless and better than the suggested alternative. Just because we find some of the IP's edits problematic doesn't mean we should go out of our way to avoid all of the IP's ideas. But otherwise I agree with the discussion above: 2048 and 4096 are potentially independently notable from the powers of two more generally, but the IP's version doesn't show it, and until someone does it's better to have them as redirects. —David Eppstein (talk) 07:12, 24 March 2020 (UTC)

Pruning number articles
I see you've dramatically cleaned up and  by removing sections tangentially linked to the number. I understand the reasons and the pages certainly look tidier, but we may risk throwing away a few babies with the bathwater. Before continuing with other numbers, do other editors have any comments? Certes (talk) 16:35, 3 January 2020 (UTC)
 * More than a few...I vehemently oppose this clean-up and strongly suggest reverting to the old (albeit lengthy) article until you can justify this kind of clean-up. Many of Wikipedia's pages are useful (in particular these numerical articles) precisely _because_ of this kind of trivia 121.208.147.104 (talk) 11:50, 4 April 2020 (UTC)

I preferred the article for 7 before the information was purged. My favorite thing about number articles has always been the mythology, symbolism, and obscure references that come in useful (especially when studying literature). Right now, the 7 article is very short and it seems arbitrary to include the mathematics section, rather than the symbolism section for instance.

Article size is important, but Wikipedia is WP:NOTPAPER and the shorter article in this case doesn't seem to make Wikipedia better in my opinion.

Excess information can be split into a different page, however, the main article should still contain sections summarizing the different topics. This is how most long articles are fixed. Pythagimedes (talk) 05:53, 23 May 2020 (UTC)
 * Unsourced cruft should be deleted, not lovingly saved and elaborated. —David Eppstein (talk) 07:07, 23 May 2020 (UTC)
 * That’s incorrect, unsourced information should be properly sourced rather than deleted (or tagged “citation needed”). If it fails verification, then it can be removed Pythagimedes (talk) 00:56, 25 May 2020 (UTC)
 * Unsourced information significant to the subject, maybe. But I said "cruft", and in this case that's mostly what it was. —David Eppstein (talk) 01:28, 25 May 2020 (UTC)

Merger proposals
Formal request has been received to merge:Lakh to Indian numbering system; and Crore to Indian numbering system. Both dated: August 2020. Proposer's Rationale: ''Been open and articles tagged for over 6 months and likely no sign of consensus. One of two dependent discussions poorly set up independently to add to mess. Needs resolution.'' Discuss >>>here<<<. GenQuest "Talk to Me" 05:50, 12 August 2020 (UTC)

Number article titles
I think it's worth mentioning for any newcomers where the number articles live. Historically, titles from 1 to about 9999 were reserved for years. Having realised that AD 1 is not the primary topic for the term "1", the articles now reside at: Further details at User:Crouch, Swale/Year DAB. Certes (talk) 13:03, 18 August 2020 (UTC)
 * , Thanks, that's useful. S Philbrick  (Talk)  14:05, 18 August 2020 (UTC)

items to be included and excluded from articles about integers
Many of our articles about integers shared two troubling shortcomings:
 * 1) a lot of entries without references
 * 2) a lot of entries that were crufty

Regarding referencing, not every single thing in an article requires referencing. The policy on original research notes an exception No_original_research for routine calculations. That said, while we don't need a reliable source to tell us that 10 is the integer between nine and 11, most of the statements in such an article don't qualify for this exception and ought to be referenced.

The more challenging issue will be to determine what statements deserve inclusion and which ones should be removed.

One of the reasons for writing this is my observation that removed about 75% of 7 in January of this year. I see that discussed above in Wikipedia_talk:WikiProject_Numbers. That removal wasn't reverted, but that removal took out material very similar to material still extant in articles such as 6 and 8.

I think that removal took out too much, but I immediately agreed that some of the articles had ventured into coat rack territory, hence this discussion.

I note that the notability criteria for existence of an article emphasizes the mathematical properties of the number. However, when talking about the appropriate material to be included in an article I would push back if anyone argued that the discussion ought to be limited to the mathematical properties. There is little doubt that there are interesting mathematical properties of 13, for example, but that number also occupies a special place in other fields, and those uses deserve inclusion. The smaller integers are going to have both interesting mathematical properties and interesting nonmathematical properties so there won't be any question about the existence of an article, but we may have to discuss what types of things belong in an article.

As examples of extremes, we have an article about the integer 1729, which exists because of its mathematical properties, and almost all of the discussion in the article relates to mathematical property. In contrast, we have an article about the integer 666, but that article exists primarily because of the existence of the number in literature, particularly religious literature. The article itself does have a discussion of mathematical properties, but probably wouldn't warrant a standalone article on that basis alone.

I'm thinking of putting something together as a standalone essay but wanted to start the discussion here.-- S Philbrick (Talk)  22:08, 15 August 2020 (UTC)


 * Essay_regarding_inclusion_criteria_for_integer_articles-- S Philbrick (Talk)  00:16, 17 August 2020 (UTC)
 * Just happened to see this (I'm really trying to limit my activity, and the ping above is broken, so it was fortunate I caught the post). Just FYI, someone copied all the stuff I cut out of the article on 7 into Symbolism of the number 7, and then trimmed some back out, but left an awful lot.  I also gutted 2 (number), to which someone added a little back (including some silly stuff, like number of strands in DNA, number of stars in a binary star system, etc).  After that, I kind of lost my stomach for this.  The smaller you get, the worse the cruft tends to be, a consequence of the Strong Law of Small Numbers.  Frankly, if there's anything to say about the symbolism of 7 for example, it should probably get merged back in, if it can be written about encyclopedically, with good sourcing.  But contextless lists of places that 7 appears, or articles that happen to contain the number 7 in their title...ehhhh.  I've mostly left the mathematical properties alone, but I think those tend to get pretty iffy too – again, especially so the smaller you get. See User talk:Deacon Vorbis/Archive 2020 for some of my thoughts while my frustration was still fresh after a particularly extreme case.  Anyway, if I get the motivation, I'll take a look at what you've written up and see if I have any comments.  Either way, good luck.  I fear Wikipedia is losing the war against cruft. –Deacon Vorbis (carbon &bull; videos) 01:04, 17 August 2020 (UTC)
 * Even 1729 (number) was getting pretty crufty. I just cut it back some more. —David Eppstein (talk) 07:41, 17 August 2020 (UTC)


 * I'm an inclusionist but these articles stand out as below our usual standards, partly due to the large number of inexperienced contributors wanting to add their favourite use of the number. As hinted in the essay, we might apply the "serial test": if a similar point could be made about most numbers within some range then those factoids probably belong together in an article about the topic rather than being dispersed over number articles.  For example, I helped to yank out the jersey numbers, putting those which merited a mention into List of retired numbers (along with their sparse citations).  We might make limited exceptions such as Wayne Gretzky and Michael Jordan but I've been reverting good-faith additions and wouldn't like to see the number pages cluttered with obscure sports players again.  We've also purged niche interests such as bingo nicknames and okrugs of Saint Petersburg which appeared on many number pages.  It might be useful to analyse a couple of typical number pages in detail and find a consensus for what it should contain, as a precedent for pruning the others.  Certes (talk) 11:21, 17 August 2020 (UTC)
 * I applaud any efforts to improve this problem. One test which would quickly dispense with the Saint Petersburg example is: "Is this a property of the number, or is it just the number in use?" I recently removed the bit from 4 about how in ASCII 4 is the code for EOT (end of transmission; archaic), on the grounds that if this is significant we need to list every major character set ever defined. Like we would have to mention London N4, NW4, W4, SW4, SE4 and so on. I have also wondered about the list of "numeral symbols", and about lists of representations in various bases. (Did you know that 4 to the base 16384 is written as 4?) Imaginatorium (talk) 18:51, 17 August 2020 (UTC)
 * , I like the formulation "Is this a property of the number, or is it just the number in use?". That's what I was getting at when I made reference to page numbers, and was my justification for removal of " The Roman numeral IV (usually) stands for the fourth-discovered satellite of a planet or minor planet (e.g. Jupiter IV)" I'm in astronomy fan but that's a bit too much. S Philbrick  (Talk)  21:04, 17 August 2020 (UTC)

Is there a distinction between articles like 1001 (number) (which, I'm guessing from the title, is about an integer and not the name of a popular British detergent in the 1960s) and articles like 9 (which is equally about a number but doesn't say so in the title and might attract text which belongs in 9 (disambiguation) or in the rubbish bin)? Certes (talk) 21:12, 17 August 2020 (UTC)
 * No, that's just to distinguish them from articles about years. —David Eppstein (talk) 22:09, 17 August 2020 (UTC)

One topic which is often repeatedly removed and replaced is gematria – a selection of words whose letter values total the title number. One example is at 19 (number). It would be useful to have consensus on whether these add value or can get out and stay out. Certes (talk) 15:26, 18 August 2020 (UTC)

Integer hatnotes
Most people are familiar with the Emerson quote:

A foolish consistency is the hobgoblin of little minds,

This quote is occasionally misstated, excluding the word "foolish". Consistency is often a positive trait, although the quote notes that it can be carried to an absurd extreme.

With that caution in mind, I decided to examine the hatnotes and the lead section of the articles about the integers between -1 and 150.

This section is about the hatnotes— I will follow up with a comparable section on the lead sentences.

The following collapse table has three sections:
 * 1) The first five rows are a legend to explain the shortcuts for various types of hat notes
 * 2) The next row is a summary count which counts how many of each type of hat note exist
 * 3) The third section is the detailed section with a header row and then detailed information for each integer between -1 and 150

No Hatnote
The most common situation (in 116 out of 152 entries) is to have no hatnote at all

Link to dab page
The next most common situation as entry "D" which means there is a link to the disambiguation page. This occurs in 38 of the 152 entries. Note that while it is very common in integers 1 – 10 and in 23 of the integers up to 25, it is oddly missing from 12 and 15. After 25 it occurs on occasion but in no obvious pattern

Hatnote "This article is about the number."
Another comments situation is denoted by the letter "N" which indicates that the article is about the number. 23 of the entries have this hatnote. It exists in all integers between one and 12, but after that appears to be haphazard whether it is included or not.

Link to Year page
A number of entries include a hatnote denoted by the letter "Y", signifying disambiguation from the article on the year. This occurs in every integer between one and 12 except for 11, and after that exist for the integer 38 and 50 but no others.

Hatnote identifying a link from a Roman numeral
Some entries disambiguate the Roman numeral, designated by the letter "R". This exists in several (but not all) entries between 16 and 26, and then again 65.

Other Hatnotes
Then there are a variety of other disambiguation pages which I haven't separately classified but denoted the model with the letter "O"

Other Hatnotes
It is far from my intention to suggest that we ought to have exactly the same treatment for all integers. Particularly the case of those marked "O" those hatnotes appear to be specifically associated with a property of that particular number. Open to any discussion but my intention would be to preserve all of those.

However, I suggest that we ought to discuss the treatment of the other entries.

Hatnote "This article is about the number."
Starting with something easy, many entries have texts such as "This article is about the number." There are some variations such as: "This article is about the number 23" or ""This article is about the number 69". I don't think there's any justification for the slightly different wording, and if we are going to include something along these lines, we ought to make it consistent. The easiest option is to stick with the most common situation "This article is about the number."

Hatnote identifying a link from a Roman numeral
Slightly more complicated is to determine when this hatnote should be used. The Roman number hatnotes are also difficult to justify as is, although there may be a rationale. This may be a little outside our scope. For example, XVII is a redirect, and thus mentioned, but XV is not a redirect. While I haven't checked them all, it might be that whenever there is a redirect, it's mentioned here but not mentioned if the Roman numeral is a dab page. That does suggest the need for discussion to determine whether those decisions (whether the characters corresponding to a Roman number should be a redirect or a dab page) ought to be rationalized. if anyone wants to take that on, go for it, and if so it will have implications for these pages but short of resolving that, I suggest we leave the Roman numeral hatnotes as is.

Link to Year page
A number of entries disambiguate from the page about the year denoted by "Y". As noted, this occurs in all entries between 1 and 12 except for 11, and then exists for 38 and 50. While it is understandable there should be no such entry for -1 and zero, I'm struggling for a clear rationale for the inclusion in numbers 1 next– 10 and only three entries after that. One option is to include everywhere, another option is to include nowhere, and yet another option is to include in some range (or defined subset) but we ought to have some rationale for the range or subset.

General discussion
The former hatnote on 17 (number), ""XVII" redirects here. For other uses, see 17 (disambiguation).", is plainly incorrect. There are no other uses of "XVII" at 17 (disambiguation). Redirects should only be mentioned in hats when an ambiguity with the redirected title is the reason for one of the hat links. —David Eppstein (talk) 19:15, 22 August 2020 (UTC)
 * I suppose AD 17 is another use of "XVII" but not of "17 (number)". Certes (talk) 19:30, 22 August 2020 (UTC)
 * It's a use of "XVII" in its meaning as the Roman numeral for 17. There are lots of those. What I meant is that no entry at 17 (disambiguation) uses the string "XVII" in its title and therefore the fact that "XVII" currently redirects to 17 (number) is totally irrelevant to the hatnote on 17 (number) pointing to 17 (disambiguation). —David Eppstein (talk) 20:46, 22 August 2020 (UTC)

Next steps
I had hoped for a more robust discussion, but my guess is that many of the contributors to the various articles did so years ago and many of the issues are largely settled.

In the absence of more discussion I'm going to take some action but I will summarize my planned action below to give one last chance for feedback.

There are a number of entries that have a hatnote very specific to the number. As an example, 49 (number) has the hatnote: For the steamboat, see Forty-Nine (steamboat).

In some of those cases, there is also the note I identified as "N", so the complete hatnote on that article is: ''This article is about the number. For the steamboat, see Forty-Nine (steamboat).''

Note that there are no current examples of the generic hatnote "This article is about the number." by itself, that is, that phrase is only used when there is another hatnotes.

I think it makes sense, when an article includes a hatnote about the specific number, to also include the generic hatnote "This article is about the number." Some do such as 49 (number). Some do not such as 28 (number).

My plan:

Number specific hatnote (identified by "O" in my list)
 * If the article has a number specific hatnote, also include the generic hatnote "This article is about the number."

Roman number redirects
 * There are seven instances of a hatnote identifying that a Roman number redirects to the page. That obviously doesn't cover all Roman numerals, but my spot checks (not exhaustive) suggests that many Roman numerals have their own dab page, V (disambiguation). I plan to retain the notices of redirect.

Link to year article
 * There are 13 instances where there is a hatnote identifying the article about the year associated with that number. I haven't come up with a coherent argument why a reader might be confused about, say "6" or "7", but not "33" or "34". I'm thinking this hatnote should either be in all or none, so I'm going with the much more common usage and going with none.

Dab hatnote
 * Many of the first few articles, i.e. all but "12" between one and 25 have a dab hatnote typically reading "For other uses, see nn (disambiguation)" it's obvious why this hatnote is included, but far from obvious why 12 (number) would not have it or why only 14 of the hundred and 25 values between 26 and 150 have it. While I am sure we have more traffic on the integers in the first 25 range, I'm betting that the traffic on all the numbers above 25 is high enough that we would've received complaints about the absence of a hatnote if that were a problem. given my inability to find a good rationale for inclusion in one range but not another range, my plan is to remove them all. We can obviously restore if we find is a good need for them.

Before actually carrying this out I have created another section below talking about inconsistencies in the lead section. If I don't get pushback on proposed changes it might be easiest if I did changes to the hatnotes and the lead section at the same time.-- S Philbrick (Talk)  23:05, 24 August 2020 (UTC)

Integer article - Lead section
Of the first 152 articles, 138 use what I call a canonical lead: nnn (text) is the natural number following nnn-1 and preceding nnn+1.

In 112 cases that's the only text (other than possibly hatnotes) in the lead section.

In a few of the 14 exceptions, I see little justification. For example in 14 (number), the text is: 14 (fourteen) is a natural number following 13 and succeeded by 15.

In other words, identical to the canonical form except using "succeeded by" rather than "preceding". My guess is that this is just an artifact of history or possibly some editor slightly preferring different wording but not looking at related articles. I think the canonical format is fine. I'm open to discussion about alternative wording but think it ought to be in general used everywhere.

In four cases, numbers two through five, a different wording is used, for example: 2 (two) is a number, numeral, and glyph. One might argue that the term glyph are to be used for 0 – 9 but not elsewhere. I can't think of a justification for using "numeral" in a handful of cases. It logically applies to all, so if it is critical for some it ought to be used in all but my preference is none.

A number of articles have some additional text in the lead such as a statement that the member is prime. While this is an important property, the standard format of these articles has a lead section, then additional sections identifying the properties. I can't think of a good reason for treating certain properties as so important that they belong in the lead when those same properties are sometimes in the body. I think this came about through the organic development of the various articles and never got cleaned up. My intention with a couple of those exceptions, is to move all these properties to the body. One exception is that two articles (67 and 68) identify that the number is odd and even respectively. Arguably an important property but also arguably so well known that it's not worth mentioning. Clearly doesn't belong in the lead and I don't intend to move that statement into the body. I plan to simply drop it.

60 (number) is the only article in this range the contains an audio file explaining how to say the number. I'm not opposed to the concept but think it ought to be in all or none. I suspect it's only in this article because that's the only file that exists, but I suggest that someone ought to undertake a project to create such files for all numbers, and if that project is completed we ought to have none. I fully understand that someone could make the argument that we don't have the other files until we do we should retain the one that we do have. If the consensus is that it should be retained I will argue but it is slightly odd that we have hundreds of articles on numbers with exactly one audio file.

Three articles, -1 (number), 0 (number), and1 (number) have more extensive leads. While I'd like to bring them into a canonical form, it isn't immediately obvious how to do that, so I'm going to restrict my changes to the range 2 – 150 at present, and we can discuss how to change those other articles if necessary at a subsequent time.

Plan summary
 * For all but -1,0,and 1 (to be discussed later), use the canonical form and only that sentence as the lead.
 * For all other information currently in the lead, move into the body, with the exception of the two articles mentioning that the number is God and even
 * Remove the single audio file

Discussion
I don't think that removing from the lead all information beyond the predecessor and successor of a number is a good idea. In many cases, there is some special significance to the number that is sufficiently prominent, beyond the other information about it, to put into the lead. For instance, in the first example I checked, 5 (number), the claim "It has attained significance throughout history in part because typical humans have five digits on each hand." is certainly lead-worthy, although not currently well backed-up by sources and by elaboration within the article text (which is a crufty collection of lists as many of these articles are). Similarly, for example, the mention of 10 as being the base of the decimal system should stay in its lead, and the mention that 12 "frequently appears in the world's major religions" belongs in the lead as an appropriate brief summary of part of the rest of the article's content. More, I strongly disagree with your reasoning that a property being well known is a good reason to not mention it — it is a good reason to mention it! The reason to drop being odd or even from numbers 67 or 68 is not that it's a well known property, but that it's not interesting as a property — it doesn't make them stand out among other numbers. —David Eppstein (talk) 23:49, 24 August 2020 (UTC)


 * Thank you for the above analysis which was sorely needed and raises several important issues.Hatnotes are mainly navigational: they exist to say that this article is about a number, and to direct anyone looking for something else to the right page. We need them when and only when the article's title or a redirect to it might also refer to some other topic.  Number articles with simple numeric titles (1–10, 100, 10,000+) require hatnotes to guide the reader to other meanings of those numbers or at least to a dab listing them.   Articles called "n (number)" usually don't, unless there is an ambiguous incoming redirect such as .I'm not a great writer of leads and don't have good evidence or even strong feelings as to the best answer for every detail.  In general, it would be encyclopaedic to have consistent defaults for content and format but to allow exceptions where they are justified.  We certainly don't need to mention common properties such as being even, and primality is covered by the infobox.  I would even question whether we need the stock phrase that 5 follows 4 and precedes 6 (a few of which I added for consistency).  Few readers capable of operating a web browser will be ignorant of those facts, and they're implied by the infobox header anyway. Certes (talk) 12:36, 25 August 2020 (UTC)
 * , Thanks for pointing out something I sort of knew but had not fully sunk in. The decision we made regarding titles means that the handling of the titles for -1 – 10 and 100 I different than for 11 – 99 and 101 –150. S Philbrick  (Talk)  16:01, 25 August 2020 (UTC)


 * I agree with David Eppstein's point about the lead - many numbers have just one or two salient properties, mathematical or not; e.g. 666 is the number of the beast (whateverthatis) and 1729 is the taxicab number. If anything, I find the boilerplate "following n-1 and preceding n+1" rather odd. Since it is more or less how the natural numbers are defined, it would be more mathematically informed I think just to say "1729 is the natural number following 1728, and is famous as..." Such a change would obviously need a clear consensus... Imaginatorium (talk) 15:12, 25 August 2020 (UTC)

(More generally, on consistency) I think it would be good to have a quite detailed "MOS" for these articles, to make it easier to make them consistent, not to enforce the iron hand of dull conformity. Another thing to look at is the "numerals" listed in the infobox. I have been going around removing a number of claimed "Korean numerals", because they are no such thing, they are simply the Korean word for the number written in Hangul (the world's most logical writing system, actually, made from hooks and boxes). There are "Chinese numerals", meaning the Han ideographs for numbers (1, 2, 3,..., 10, 100, 1000, 10000 (missing!), 1,0000,0000...; but then many of these have variant forms, including some Japanese variants, which could be called "Han ideographs", but not quite "Chinese characters". A guideline would help. Then there are lots of languages I know nothing about, but the Bengali "numeral" (and many others) for 100 is simply the number written in decimal notation. Mustn't ramble, but this is quite a large topic... Imaginatorium (talk) 15:46, 25 August 2020 (UTC)
 * , I'm not a big fan of dull conformity, but I see it as a modest step ahead of quasi-random inconsistency. Having argued that stating that a number is odd or even is too basic, I can hardly argue that the claim that "n follows n -1 and is succeeded by n +1" deserves mention. I think that's an excellent point and would like to see us settle on a better option. I'm happy to see a little more involvement in this discussion and I'm going to hold off making any changes to any articles until we have a more thorough discussion. S Philbrick  (Talk)  16:08, 25 August 2020 (UTC)
 * My point (perhaps not well expressed) was that the guideline could be very specific and detailed, yet be a guideline, so that in any special case it can be overwritten. And about "successor": one way of defining the natural numbers mathematically is to say something like: (a) 1 is a natural number; (b) if n is a natural number there exists a successor of n, i.e. n+1. So by saying "47 is the natural number following 46" we give a chain of definitions leading us back to 1. Imaginatorium (talk) 19:37, 25 August 2020 (UTC)

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Angel numbers
Several numbers (mainly repdigits) are described prominently as "angel numbers". The cited sources do not seem mainstream. Should we remove such claims? (My search returns a few false positives.) Certes (talk) 22:56, 2 July 2021 (UTC)
 * ✅ Another editor has now removed them. Certes (talk) 17:05, 3 July 2021 (UTC)

Why I think GOD = 786 = Atom?
A third opinion on whether to add certain content to 786 (number) would be welcome at Talk:786 (number). Certes (talk) 11:28, 18 July 2021 (UTC)

redirect request
I was unsure whether to accept this redirect request (from 200,000 to 900,000 → 100,000). &#8213; Qwerfjkl  talk  17:21, 31 August 2021 (UTC)
 * 100,000 has doubled in size over the last couple of days and could sensibly be split – but only if we're going to keep the new material, which is being discussed in the previous section. Certes (talk) 17:56, 31 August 2021 (UTC)
 * @Certes Just checking if this has consensus before accepting at WP:AFCRC. (All the X00,000 articles have been created.) &#8213; Qwerfjkl  talk  17:50, 4 September 2021 (UTC)
 * All of these redirects about numbers at Articles for creation/Redirects and categories are requested by me. Can you accept this? 176.88.30.25 (talk) 17:59, 4 September 2021 (UTC)
 * I'm not sure if @Robertsky (the drafts' reviewer) is aware of the above discussion. &#8213; Qwerfjkl  talk  18:02, 4 September 2021 (UTC)
 * We're still discussing the inclusion of squares in the previous section. They are far more common than other properties which justify inclusion.  It's only the massive expansion of 100,000 by adding squares that makes it a candidate for splitting. Certes (talk) 18:41, 4 September 2021 (UTC)
 * , feel free to turn the new articles into redirects or AfD if needed after the discussion ends? I don't mind. – robertsky (talk) 20:30, 4 September 2021 (UTC)
 * The IP who is the mover behind all of this has been blocked by a checkuser; their additions are pure cruft, and there is a clear consensus above to revert the additions. Then any splitting they did should almost certainly be reverted, as well. —JBL (talk) 13:09, 8 September 2021 (UTC)
 * "pure cruft" is a little harsh. Clearly this IP tried to contribute and was over-zealous about what and how much to contribute. We shouldn't be discouraging his efforts. Some day he may contribute something more useful. Dhrm77 (talk) 11:15, 9 September 2021 (UTC)
 * Agreed. These are good-faith edits that a specialised wiki would welcome.  They're only slightly too detailed for Wikipedia, which is why I sought a second opinion before removing them.  It's not typical fancruft like who voiced Dalek #42 in the Latvian dubbing of Trek Wars; it's basic and useful mathematical fact.  If this came from a registered account, we would nurture and guide.  That's harder with someone who hops IP (probably involuntarily).  On the other hand, the IP has a checkuser range block, so there may be more to this than meets the eye.  Certes (talk) 12:11, 9 September 2021 (UTC)

Squares
Most of 100,000 consists of new entries of the form Is being a perfect square a sufficiently notable property to merit a mention in number range articles? Certes (talk) 18:51, 30 August 2021 (UTC)
 * 101,124 = 3182
 * I'm continued to make all perfect squares up to 1000 but beyond 500k coming soon. 176.88.30.25 (talk) 19:02, 30 August 2021 (UTC)
 * This wasn't what Certes was asking... Dhrm77 (talk) 16:14, 31 August 2021 (UTC)
 * I think, what Certes was asking (to the general wikipedia reader interested in numbers) was: "Is being a square, (and/or being a prime) enough of a characteristic to be mentioned in a number article?" Historically, a number has been listed for having at least 2 properties, like being a prime and something else, or being a perfect square and something else. For prime numbers, their occurrence is frequent. Squares are less frequent, but still quite abundant. Dhrm77 (talk) 16:14, 31 August 2021 (UTC)
 * I agree with the principle that it takes multiple significant or interesting properties to make a number individually notable. Square primes, for instance, would definitely be notable. —David Eppstein (talk) 17:13, 31 August 2021 (UTC)
 * Yes, that's what I was asking. Squares of primes are certainly rarer and thus more noteable, though it's still only one property.  Certes (talk) 17:52, 31 August 2021 (UTC)
 * I did not say "squares of primes". —David Eppstein (talk) 18:37, 31 August 2021 (UTC)
 * Wait, i'm confused... If "Square primes" doesn't mean "squares of primes", then what does it mean? It can't obviously mean "squares that are also prime", since that's mutually exclusive, unless that was a sarcastic statement. Dhrm77 (talk) 17:30, 1 September 2021 (UTC)
 * unless that was a sarcastic statement More a joke, really, but I guess if I have to explain it... —David Eppstein (talk) 18:28, 1 September 2021 (UTC)
 * Then I have to agree – a square prime would definitely be notable. In fact, I'd say it deserves a whole article to itself.  Certes (talk) 18:43, 31 August 2021 (UTC)
 * We should separate the "X00,000 to X99,999" sections to a different page: 200,000 to 299,999 should be 200,000 for example. 176.88.30.25 (talk) 19:51, 31 August 2021 (UTC)
 * I tend to agree with Certes, and disagree with you. Being a square is not by itself enough to be listed. We should clear out this newly added cruft instead of expanding and splitting off. —David Eppstein (talk) 19:53, 31 August 2021 (UTC)
 * I made 8 more drafts. If they were accepted, then I will remove 200k to 900k from "100,000". 176.88.30.25 (talk) 08:41, 3 September 2021 (UTC)

Survey on squares
In number range articles such as 100,000, should we keep or delete numbers where the only property mentioned is being a square? Certes (talk) 21:14, 4 September 2021 (UTC)
 * Delete per @Dhrm77: Historically, a number has been listed for having at least 2 properties, like being a prime and something else, or being a perfect square and something else. For prime numbers, their occurrence is frequent. Squares are less frequent, but still quite abundant. &#8213; Qwerfjkl  talk  21:21, 4 September 2021 (UTC)
 * Delete. They fail Notability (numbers), which asks for three independent and interesting properties of each number. 1 < 3. —David Eppstein (talk) 23:25, 4 September 2021 (UTC)
 * Keep because the squares of many numbers from 101 to 1000 were added by me. 176.88.30.25 (talk) 11:31, 5 September 2021 (UTC)
 * we need a better reason than because 'it was me' on why we are to keep the numbers. – robertsky (talk) 12:15, 5 September 2021 (UTC)
 * Agreed, "because it was me" is hardly a reason. Dhrm77 (talk) 00:57, 6 September 2021 (UTC)
 * Delete, or find a additional properties of interest to justify keeping specific examples. XOR&#39;easter (talk) 17:06, 5 September 2021 (UTC)
 * Delete most of them, but let's see if we can find additional interesting properties for some of these before deleting the rest. Also, I would say that asking for 3 distinct interesting properties might be a little excessive. Some properties are so unique that they justify listing a number just by themselves. Dhrm77 (talk) 00:57, 6 September 2021 (UTC)
 * A number requires three properties to earn its own article. The bar for a list entry will be lower; we're deciding how low. WP:Notability (numbers) requests a property that is interesting enough.  Whether being square or prime is "interesting enough" is subjective, but I lean towards No.  Certes (talk) 11:32, 6 September 2021 (UTC)
 * Delete. Squares are not interesting enough to list so many and dominate the lists. PrimeHunter (talk) 20:57, 6 September 2021 (UTC)

Survey on primes
Should we keep or delete lists of primes such as that at the end of 10,000? Certes (talk) 21:14, 4 September 2021 (UTC)
 * Delete per my comment above. &#8213; Qwerfjkl  talk  21:21, 4 September 2021 (UTC)
 * Delete. They fail Notability (numbers), which asks for three independent and interesting properties of each number. 1 < 3. —David Eppstein (talk) 23:26, 4 September 2021 (UTC)
 * Delete as unhelpful clutter, the mathematical version of indiscriminate trivia. XOR&#39;easter (talk) 17:09, 5 September 2021 (UTC)
 * Delete. Primes are very notable and studied, and in February I added nine similar lists at 1000 (number) to 9000 (number), but they only use around five lines on desktop. Ten times as much is too much. The list of prime numbers in 10,000 is longer than the one in List of prime numbers. That's a little absurd. PrimeHunter (talk) 20:53, 6 September 2021 (UTC)

Reverting
The surveys seem unanimous apart from the IP editor, who is now blocked. I'll take that as a mandate to restore the pre-square version of 100,000 and replace the new articles by redirects. Then I'll set about reverting the edits to other number ranges – help welcome! Certes (talk) 13:22, 8 September 2021 (UTC)
 * Progress so far:
 * 1,000,000,000; 100,000,000; 10,000,000; 1,000,000: edits seem reasonable; not reverted
 * 100,000 to 900,000: merged, with repairs to all the incoming wikilinks and redirects I could find
 * 90,000: reverted, though I may have thrown a few good edits from the same IP range away too
 * 80,000, 70,000: reverted
 * An IPv6 range has recently made similar additions, which complicates things. I'll pause there overnight, in case anyone finds problems.  Certes (talk) 01:19, 9 September 2021 (UTC)
 * Number pages from 10,000 upwards are now restored. I've also removed similar contributions from the rest of 176.88.28.0/22 and from 85.153.228.230, 2806:109f:9:241d:e990:ff0f:a8d9:fe2 and others.  Thanks for all the advice and help.  Some reversions were intricate due to intervening improvements and vandalism from other sources, so I'd appreciate someone checking my work. Certes (talk) 11:42, 9 September 2021 (UTC)

Numbers below 10,000 contain (I hope) fewer than 100 squares spread across many pages. There are lists of primes, but again they're relatively short. 94.59.203.163 has expanded these pages with edits like. How much of this should we be reverting? Certes (talk) 11:42, 9 September 2021 (UTC)
 * I looked at a few of these pages below 10000, and haven't seen anything to revert. Perhaps you're done. Dhrm77 (talk) 18:31, 9 September 2021 (UTC)

Fractional factor vandal
Fractional factor vandal is back on 156.3.33.28. Reported to AIV. I try to wait for a block before performing my third reversion on each page, but I'd appreciate someone reviewing recent edits to 800 (number) as I've accidentally reached my limit there already. Certes (talk) 21:43, 8 November 2021 (UTC)
 * AIV entry removed, but all edits reverted and they seem to have stopped for now. Certes (talk) 22:53, 8 November 2021 (UTC)

20,000.00
What is that dollar amount 20,000.00 98.186.161.208 (talk) 16:40, 17 November 2021 (UTC)
 * To question an amount which appears on a Wikipedia page, please open a discussion on its own talk page. Certes (talk) 17:16, 17 November 2021 (UTC)

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-, =, or self revert?
Should the numbers be all like: Or like: Or should I self revert, which makes: — Preceding unsigned comment added by Viewer719 (talk • contribs) 12:55, 29 April 2022 (UTC)
 * 123 = primordial prime
 * 142 = 8169
 * 123 - primordial prime
 * 142 - 8169
 * 123 - primordial prime
 * 142 = 8169

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