Talk:Interesting number paradox

The set is defined as uninteresting
The numbers in the set are defined as uninteresting. Redefining a number in the set as interesting cannot be done since a set is specifically defined. Saying that an uninteresting number is interesting because it is the smallest number of an uninteresting set is to say the set is improperly defined, making the paradox moot. The number is uninteresting by definition. Saying the number is "smallest" and therefore "interesting" is inconsequential. — Preceding unsigned comment added by 184.10.252.162 (talk) 05:50, 28 November 2013 (UTC)
 * The point is that the set cannot be well-defined. Although one could comment that if A is the smallest member of the set, which makes it interesting and therefore not in the set, where does that leave A? It's no longer interesting because its reason for being interesting is now invalid. -mattbuck (Talk) 08:56, 28 November 2013 (UTC)
 * That goes against the definition of a set. A set, by definition, is well defined. It is impossible to have an interesting number in an uninteresting set, if and only if there is a defined set of interesting numbers outside of the uninteresting set. Therefore, saying a number is interesting therein is fallacious. However, even if there is a subset of interesting numbers the fallacy is in the assumption that there is a set outside of the uninteresting set with the same definition. Again, this defeats the purpose and disregards the definition of a set. Merely saying a number is interesting is not enough, once it has been defined it is done; such is the definition. The paradox only comes in if you allow yourself to distort the definition of the set for the purpose of the paradox, which is again, a fallacy. — Preceding unsigned comment added by 184.10.252.162 (talk) 17:11, 30 November 2013 (UTC)

Interest is an emotion, not a number
Both interest and uninteresting is not a paradox. it is like being bored of something exciting, or sad that you'll never be this happy again. Emotions cause their opposites all the time, so there is no paradox. —Preceding unsigned comment added by 76.204.97.52 (talk) 05:38, 6 December 2008 (UTC)

Analysis
(Copied from 1729 number discussion page - the comment seems more pertinent here)

a) Should the statement that a number is interesting because it is the smallest uninteresting number be treated as an axiom? Acceptance or rejection of the axiom would be a matter of individual choice. Xenoglossophobe


 * Agreed, so I disagree with the artcile's statement that
 * there would be a smallest number with no interesting properties (for instance, 38 could be a candidate). This in itself would be an interesting property of the number, so it would no longer be dull.
 * &mdash;msh210 18:20, 18 Nov 2004 (UTC)

b) As the application of this putative axiom to the smallest uninteresting number leads to its removal from the list of uninteresting numbers and places the next lowest uninteresting number in a similar position that also requires its removal (and so on, ad infinitum), should this be regarded as proof by mathematical induction rather than proof by contradiction? Xenoglossophobe


 * I wouldn't call it an axiom, it's more a definition. It could be made into a proof by induction, but it is currently expressed as proof by contradiction.  "Say we wish to prove proposition p. The procedure is to show that assuming 'not p' (i.e. that p is false) leads to a logical contradiction. Thus p cannot be false, and must therefore be true."  P is "there is no smallest uninteresting number."  We assume not p (there is a smallest uninteresting number), and show the contradiction.  Therefore p. A proof by induction would work completely differently.  anthony (this comment is a work in progress and may change without prior notice) 21:46, 29 Mar 2004 (UTC)


 * The suggestion is made based on the following understanding of the prinicple of mathematical induction: induction requires a) the demonstration of some property of the first item in a list (which, I agree, has has been claimed in this particular case using contradiction) and b) the demonstration of a chain of implication in which the presence of this property in a general item in the list implies the presence of the same property in the next item, such that the implication extends to every member in the list, even one of infinite length. Xenoglossophobe


 * All cases have been shown by contradiction. If there is no smallest uninteresting number, then there must not be any uninteresting number.  I'd say that step is obvious.  I guess you could form an inductive proof for it, though. anthony (this comment is a work in progress and may change without prior notice) 22:20, 29 Mar 2004 (UTC)

Kudo
Most hilarious Wikipedia article I've ever read. Bravi, tutti! Ventura 23:46, 2004 Oct 14 (UTC)

Resolvable?
Removed:
 * This paradox is, however, resolvable. It may be noted that in this example 38 is the infimum for the set of dull numbers: while not dull itself, there are no dull numbers less than 38.

This is not a resolution of paradox. It is a treachery, done by substituting the definition. What kind of logical fallacy is this? Mikkalai 23:56, 26 Oct 2004 (UTC)

Cleanup notes
(text moved here from Cleanup/October)


 * Interesting number paradox a mathematician has to rewrite this article away from its sensationalist, rather than encyclopedic style. Some statements are plain false if under scrutiny (I've already removed the most evident one). Mikkalai 00:03, 27 Oct 2004 (UTC)
 * It's just a poor, thin thing - I don't see any future in it. Charles Matthews

Added tag, but IANAM. --Jim Henry 20:11, 15 Feb 2005 (UTC)

Why is this page so serious?
This page is written as if the Interesting number paradox is a serious mathematical concept which actually proves something. It's meant to be fun. People reading this artcile will get the impression that there are no uniteresting numbers and that this has been proven mathematically!--Heathcliff 23:35, 17 May 2005 (UTC)

It isn't a paradox! It's a proof that there are no dull elements of a well-ordered set.--SurrealWarrior 02:37, 29 July 2005 (UTC)

Yes, well... it is a "paradox" in an intuitive sense that "we all know that numbers can't all be interesting," but we cannot find the smallest dull one -- perhaps, SurrealWarrior, it's a proof that the natural numbers are not a well ordered set? (ha ha, just joshing). Anyway, the tone is a bit too stony-faced: an encyclopedia article should let the reader in on the joke. I think Martin Gardner came up with the idea, and the great man often wrote tongue-in-cheek about perfectly serious mathematics. This paradox is semi-serious. Since the idea of "interesting" is so very subjective, this will never be really serious; and yet the self-referential nature of the paradox follows in the footsteps of many paradoxes that rely on naive set theory. And to paraphrase Martin Gardner, this last sentence of my comment is totally uninteresting, so I say don't even bother to read it. :-) --LandruBek 05:26, 24 April 2006 (UTC)

Encyclopedias are not joke books
Note: added tone template--Keer lls ton 11:43, 8 December 2007 (UTC)


 * Every interesting encyclopaedia contains at least one joke. Otherwise a given encyclopaedia is uninteresting. (That is notwithstanding that it might be the smallest uninteresting encyclopaedia and all the ensuing logical consequences inconvenient to this line of argument given the immediate neighbourhood of content with respect to the family of all interest-driven finite random walks.) --125.253.44.20 (talk) 13:35, 21 October 2013 (UTC)

Regarding "human knowledge is countable and finite"
What could possibly be the justification for such a strong claim? I propose it be removed until justified. 17:09, 10 October 2005 (UTC)
 * Under normal assumtions about the way the Universe works humans cannot have infinite amounts of knowledge. You cannot learn an infinite number of things, because that would generate an infinite amount of heat and require an infinite amount of energy.  Tbjablin 22:31, 14 November 2005 (UTC)
 * I feel you presume too much, largely through fuzzy definitions. If "human knowledge" is meant to be interpreted as some abstract list of facts determined to date then it is of course countable but I believe this is discretizing/modelling what we actually mean by "human knowledge".  I would concede this latter thing is naturally bounded but strictly uncountably infinite.
 * If human knowledge does not mean the union of the set of things known by each human, I don't know what else that term could mean. Also, even if human knowledge were infinite, I think it still would be countable.  The set of all strings in any alphabet is coutable.  Tbjablin 12:27, 19 December 2005 (UTC)
 * I don't think human knowledge is finite or countable at all! For example, here is the title of a trivial list of uncountably many things that I know: For all real numbers x, there exists a real number y such that x+y=0. Replace x with any real number--all uncountably infinitely many of them--and you get a fact that is a part of human knowledge. That is, there are uncountably many facts that fit the stated format, and each one is something that is known by humans.  — Preceding unsigned comment added by 73.193.144.19 (talk) 18:55, 18 June 2016 (UTC)
 * Nope, that's a single fact. — Preceding unsigned comment added by 98.219.84.14 (talk) 21:54, 24 December 2020 (UTC)

Surreal numbers
Similarly, I removed the mention of surreal numbers. I don't see how they could have anything to do with the interesting number paradox. There are sets smaller than the surreals that are not well-ordered. Isomorphic 22:48, 13 November 2005 (UTC)

197.3341 is a singularly bad example of an uninteresting real number
because it is one of the very few real numbers that have been used throughout history to illustrate the concept of an uninteresting real number. Dmharvey 03:17, 12 March 2006 (UTC)


 * I think the problem here is that any number given as an example of an uninteresting number would in itself be interesting, by virtue of being singled out as an example of an uninteresting number. When I read 197.3341 as an example of an uninteresting number, I immediately assumed it was the author's intent that this, in itself, be a paradox. BGreeNZ 04:28, 11 April 2006 (UTC)

Smallest uninteresting numbers in Wikipedia
As of 30-May-2006:
 * The smallest integer in Wikipedia without its own page was 201
 * The smallest integer about which there was no comment apart from its factors was 237
 * The smallest integer not mentioned was 1004
 * Uh...203.184.25.49 08:32, 31 January 2007 (UTC)

As of 22-March-2015: Wikiditm (talk) 11:30, 22 March 2015 (UTC)
 * The smallest integer in Wikipedia without its own page was 247
 * The smallest integer about which there was no comment apart from its factors was 275
 * The smallest integer not mentioned was 1003

As of 13-June-2020: GenericName1108 (talk) 22:00, 13 June 2020 (UTC)
 * The smallest integer in Wikipedia whose article contains no visual supplements of any kind was 14
 * The smallest integer in Wikipedia without its own page was 262
 * The smallest integer about which there was no comment apart from its factors was 275
 * The smallest integer not mentioned was 1003

As of 4-January-2022: Magicalr2d2 (talk) 04:57, 4 January 2022 (UTC)
 * The smallest integer in Wikipedia whose article contains no visual supplements of any kind was 14
 * The smallest integer in Wikipedia without its own page was 262
 * The smallest integer about which there was no comment apart from its factors was 275
 * The smallest integer not mentioned was 1006


 * As of 24-February-2023:
 * The smallest integer in Wikipedia without its own page was 198.
 * (How did it lose its page?) Dectangle (talk) 15:33, 24 February 2023 (UTC)
 * Articles for deletion/198 (number) —David Eppstein (talk) 16:03, 24 February 2023 (UTC)
 * 198 (number) Hisirmynameismahbeer (talk) 00:22, 20 June 2024 (UTC)

Does not prove that all numbers are interesting
Ok, suppose 38 is the smallest uninteresting number, but by virtue of being the smallest uninteresting number, it is therefore interesting. Fine. And then 39 is the smallest uninteresting number, so it becomes interesting as well... um... what about 38? If 39 is the smallest uninteresting number, 38 no longer is, and so 38 is no longer interesting. But then it becomes the smallest uninteresting number again, so 39 goes out and 38 comes back in. You can't have two smallest uninteresting numbers, so only one number can be made interesting for this reason.

So there's a paradox, yes, but this paradox stops the chain dead in its tracks. 38 and 39 will keep switching places, but this roadblock prevents the logic from being extended to 40, 41, 42, etc. So there is a major problem with trying to say that this proves that all numbers are interesting. Argyrios 17:36, 4 June 2006 (UTC)


 * I think it would be quite interesting if both 38 and 39 were the smallest uninteresting number. Dmharvey 02:18, 5 June 2006 (UTC)


 * lol. Sure, "if," but the point is they can't both be. There can only be one "smallest uninteresting number," so you can't say that every uninteresting number is actually interesting by virtue of being the smallest. Or, you know what, let's just say for the sake of argument that you can have multiple "smallest uninteresting numbers." Now there is a different problem: You can't just forget about why you made the previous numbers interesting. If you have this whole smorgasbord of numbers that are supposedly all interesting because they are all the smallest uninteresting number, then it's no longer particularly special to be the smallest uninteresting number, is it?
 * I tend to regard the smallest uninteresting number as an honorary degree which didn't involve passing any exams. MaxEnt 21:02, 15 June 2006 (UTC)


 * If 38 and 39 are in some kind of quantum state of uncertainty over being the smallest uninteresting number (like Schrödinger's cat is both living and dead at once), then perhaps that would make 40 interesting as the lowest definitively uninteresting number not part of this fog of uncertainty... but making it so brings it into the fog itself, and then you can extend this by induction upward. *Dan T.* 14:21, 12 May 2007 (UTC)

Flaw who says the smallest uninteresting number is interesting on that basis?--Keer lls ton 11:45, 8 December 2007 (UTC)

I seriously don't see the problem, 38 can be the smallest uninterresting number, AND for that; be interresting, at the same time. See: Schrödinger's cat. —Preceding unsigned comment added by 194.144.18.242 (talk) 20:20, 14 September 2008 (UTC)

Origin
I'm trying to track down the source of this paradox, but I haven't had any luck yet. Chris Caldwell traces it back to a letter of G. G. Berry (0000206 in the Russell Archives of McMaster University) and calls it Berry's paradox: "You will often find Berry's paradox stated as 'every integer is interesting.'". I think Berry's paradox is usually understood to be the proof about the smallest number definable in less than X words/letters/keystrokes, though, and from a quick Google search it appears the letter is about this paradox.

The article suggests that Gardner may be the origin of this paradox. Any thoughts? CRGreathouse (t | c) 23:29, 16 September 2006 (UTC)


 * I read it in a Swedish book at least 20 years ago. I don't know it if was a Swedish original or an translation. The paradox was that there are not an least interesting integer. The book was about popular mathematics and if I remember correctly that story was about 2 mathematicians that made a cab ride and the number of the cab was dull. I just found that number, its 1729 as mentioned in this discussion page http://en.wikipedia.org/wiki/1729_%28number%29 . I guess that the paradox was written in association with that story. —The preceding unsigned comment was added by 81.231.32.208 (talk) 15:44, 21 April 2007 (UTC).

I first heard it as a humorous "folk theorem" at the Univ. of Calif Berkeley Math Dept. in about 1970. peter (talk) 01:20, 30 January 2009 (UTC)

Dull numbers
Is the last paragraph about dull numbers WP:OR? I haven't heard about them before, and the reasoning about uninteresting properties is rather contrived. You might certainly argue that unknown properties are uninteresting rather than interesting - besides the previous paragraph attempted to formalize the "interesting"-predicate as a finite list of properties, which contradicts the assertion that there should be an infinite number of interesting properties.

Unless someone objects, I will remove the paragraph in a few days. Rasmus (talk) 12:42, 9 January 2007 (UTC)


 * No comments, so I removed the paragraph. Anyone interested can read it here. Rasmus (talk) 13:02, 12 January 2007 (UTC)

Hey, I made a completely logical, true, and relevant edit and it was removed because it wasn't sourced. Can I please put it back in? --74.134.8.244 02:34, 28 May 2007 (UTC)


 * That depends. If you have a source for it, yes.  If not, the best thing to do would be to mention it here on the Talk page so someone can find a source.  CRGreathouse (t | c) 05:51, 28 May 2007 (UTC)


 * Theorem: All numbers are boring.
 * Proof: Suppose there exists a first non-boring number. Who cares? 220.255.1.22 (talk) 04:19, 4 July 2011 (UTC)

Tone
I just stumbled onto this page, and as far as I can see, there's nothing the matter with its tone. I therefore removed the template. --Slashme (talk) 06:46, 17 July 2008 (UTC)

Refutation of a proposed resolution in the article
The article says:


 * One proposed resolution of the paradox asserts that only the first uninteresting number is made interesting by that fact. For example, if 39 and 41 were the first two uninteresting numbers, then 39 would become interesting as a result, but 41 would not since it is not the first uninteresting number. However, this resolution is invalid, since the paradox is proved by contradiction: assuming that there is any uninteresting number, we arrive to the fact that that same number is interesting, hence no number can be uninteresting

Is this refutation original research? It just reiterates the original argument, so in that sense it isn't, but what I mean to ask is whether this is commonly considered to be "the" refutation of the proposed resolution. It is awfully uncharitable to assume that whoever proposed the resolution did not understand the paradox at all!

A more charitable way to interpret the resolution is that it rejects the premise that the least uninteresting number is interesting. Let us call the broadest sense of interesting "ordinarily-interesting". There is another sense, the obviously-interesting, which is something like "is a prime number or ...", which is the starting point. Then there is the meta-interesting, which is "any number that is obviously-interesting or is the least number that is not obviously-interesting". Then you analogously have meta-meta-interesting, and more generally metan-interesting. The resolution, as I see it, says that any meta-interesting number is ordinarily-interesting, but that the same may not hold for metan-interesting numbers with n > 1. Further, for none of these x-interestings does it automatically hold that a number is x-interesting if it is the least number that is not x-interesting, so the original argument fails in this more fine-grained model of interestingness. The resolution simply says that this is a more realistic model. -- Coffee2theorems (talk) 17:04, 12 February 2010 (UTC)


 * It relies on logical induction anyway, even not the more general mathematical induction. For to prove that if p and f(p), f being "the next uninteresting number", one must define f, which this does not do; indeed cannot without resorting to a higher-order logic where we can define "uninteresting", which is of course the entire point. Give that p is uninteresting, f(p) must also be uninteresting, or rather, some function of uninteresting (such as negation), but it doesn't define that function or attempt to: it might be "f(p) = slightly less interesting(p)" or f(p) = "a cow on a bicycle". Si Trew (talk) 23:26, 9 April 2010 (UTC)

Replace "interesting" with having a unique property
Start with a group of numbers that have a unique property; being the lowest number that isn't in that group is a unique property. No need for an "emotional opinion" about numbers. --TiagoTiago (talk) 04:51, 29 October 2011 (UTC)
 * Nice try, but not having a unique property is a unique property in itself, and thus the paradox remains. Only if you define "having a unique property" as explicitly excluding "having no other unique property than not having a unique property", you can resolve the paradox. Stated more simply, the lowest number which is only "interesting" (or, more precisely, "not completely uninteresting") by virtue of being the lowest otherwise "uninteresting" number is what we are after.
 * The paradox arises through defining the property "lowest uninteresting number" as inherently a matter of interest. Personally, I'd say the LUN is not altogether uninteresting, but in a different way than other numbers. It's like being famous for not being famous because you're the oldest, tallest, richest, smartest or strongest known non-famous person, for example: that is a different kind of fame. Being older, taller, richer, smarter or stronger than any famous person is more of a curiosity than what we usually think of fame. Media don't report on people with such properties, according to my experience. It's not considered inherently newsworthy, even if this person could be determined with precision. Just being very old, tall, rich, smart or strong doesn't inherently make you a celebrity; certainly not a universally acknowledged one. Only being the most extreme known example overall (Xest person living, or Xest person of all times, or Xest person of a country) could do that (and still I'd think most people would dispute that these people are actually celebrities the exact same way other celebrities are celebrities; they're just random people who usually haven't done anything particularly interesting). For this reason, I don't think the LUN is really inherently interesting just like the lower numbers; it's really kind of dull. That's also because not being inherently interesting makes this number appear random and its interest completely a matter of accident, just as accidental as in the non-celebrity "celebrities" above. You can be famous for being famous, but not for being nothing else but non-famous.
 * More importantly, this would not realistically make people interested in what the next higher otherwise uninteresting number is. If 1003 is the LUN, who cares if 1004 is also uninteresting? --Florian Blaschke (talk) 17:13, 5 February 2016 (UTC)

Smallest uninteresting number
well what is it - 11630 12067 or 12407? Kittybrewster  &#9742;  00:14, 13 November 2011 (UTC)

If we define that there cannot be a smallest "uninteresting" number as there is no smallest number, the paradox cannot continue — Preceding unsigned comment added by 204.38.188.254 (talk) 15:26, 13 January 2012 (UTC)

12407
As mentioned here, 12407 does appear in the On-Line Encyclopedia of Integer Sequences, at least implicitly, as it is a semiprime, i.e. 12407 is the product of two prime numbers. See oeis:A001358. This refutes the claim made on the main page. --Craw-daddy &#124; T &#124; 11:49, 14 November 2011 (UTC)

Nathaniel Johnson Blog a reliable source?
The citation for the claim that 12407 is the first interesting number is taken from Nathaniel Johnson's Blog. Is this really a suitable source to be referenced in a Wikipedia article? For reference: Johnston is according to the blog a PhD student. --Colapeninsula (talk) 16:37, 14 November 2011 (UTC)

Obvious flaw
I'm sorry, but if the smallest uninteresting number is interesting, then it's no longer the smallest uninteresting number, and since there was nothing else interesting about it, that means it's not interesting. Which makes it the smallest uninteresting number again, which makes it interesting again. Which makes it not interesting, which makes it interesting, which makes it not... (Note: the previous probably counts as original research, so don't add it to the article.) Xtifr tälk 10:34, 10 April 2012 (UTC)


 * No, it's a legitimate proof strategy. See also Euclid's theorem for an analogous proof that there are infinitely many prime numbers.  For more background, see Proof by contradiction.  2620:0:1000:3002:BAAC:6FFF:FE91:91CB (talk) 19:23, 3 January 2013 (UTC)

There are objectively interesting aspects of countable sets.
There are useful and therefore interesting numbers in any countable set. Take statistical measures for example, the median, mean, max, and don't forget min, are the most studied and useful numbers. Saying that these numbers are not interesting is like saying that sex isn't interesting. If you don't find sex interesting you are either mentally handicapped (and therefore inhumane) or otherwise lying (which is the likely case). — Preceding unsigned comment added by 71.220.59.235 (talk) 04:25, 20 October 2013 (UTC)

Consequences for computer science
James Gleick mentions this issue in chapter 12 of his 2010 book "The information". If we define 'interesting' as any number X being representable by a computer program that can be encoded in less information than X (see Turing numbers), then the first interesting number becomes the first number which cannot be encoded in such a way. A small modification to the programming language (the addition of the function UNINT(x) may then allow this idea to be encoded in less information than X.

Unlike the article's uninteresting property, this has built in limits - presumably it cannot be extended indefinitely without making the program encoding expand (due to the addition of new symbols or functions) so that that the new encoding for f(X) exceeds the size of X. This obviously parallels Shannon's statements about the limits of lossless compression.

Have added the book to the 'further reading' section. — Preceding unsigned comment added by 69.181.137.62 (talk) 18:59, 25 October 2013 (UTC)

Flawed
What proof is there that a "smallest uninteresting number" exists? If you pedantically insist on only looking at natural numbers, then sure; but uninteresting fractions and negative numbers would surely exist, too. 131.191.13.63 (talk) 02:31, 24 December 2013 (UTC)
 * There isn't a proof that such a number exists, that it does is taken as a point of contradiction in the proof - you assume it exists, find it leads you to a contradiction and thus prove it does not in fact exist. You could apply the same logic to the positive real numbers as they are well-ordered (exactly one of a>b, a=b, a<b holds) and have a minimum. As for negative numbers, it doesn't particularly matter what number you first define as the lowest uninteresting number, the proof works the same. Suppose you choose smallest meaning the least |a|, then you run into difficulty. For real numbers it's fine - suppose that, without loss of generality, -1 and 1 are in our set of uninteresting numbers. They both have absolute value 1, so neither can be described as smallest. However, suppose we go with -1 first, and show that it is after all interesting, then -1 is left as being the smallest uninteresting number, and voila it's interesting. However, if you go with complex numbers, then you'd need uncountably many steps to show that all numbers on the unit circle were interesting. But, you could instead just return to the positive real case, which is analogous to the complex case restricted to numbers $$re^{i\theta}$$ for some fixed $$\theta$$. Each smallest number on such a ray can be proved to not be the smallest uninteresting number on that ray, and that is something interesting about it in the whole plane. -mattbuck (Talk) 09:53, 24 December 2013 (UTC)
 * This section is somewhat off-topic, as the article specifically states that it refers to natural numbers. However, I'm not at all clear what Mattbuck means by "For real numbers it's fine", since there is no guarantee that a subset of the real numbers must have a least element. You can't just pick two real numbers (such as 1 & -1) and say that doing so is done "without loss of generality", because you are assuming that there are two numbers in the set with minimal absolute value, which is a substantial loss of generality. JamesBWatson (talk) 11:07, 24 December 2013 (UTC)

Another attempt to resolve the paradox.
All of these above "proofs" assume that interesting and uninteresting are mutually exclusive. If we don't assume that, all sorts of numbers become both. — Preceding unsigned comment added by 124.184.249.196 (talk) 02:12, 3 February 2014 (UTC)

Underlying premise
The whole paradox seems to rest on the idea that being the smallest uninteresting number is an interesting quality. What if one finds the idea of the smallest uninteresting number simply tedious? 203.217.150.76 (talk) 04:26, 6 March 2014 (UTC)
 * Simple - one then becomes a Wikipedia editor. 67.187.119.225 (talk) 04:26, 4 May 2015 (UTC)

Second-Smallest Uninteresting Number
"One proposed resolution of the paradox asserts that only the first uninteresting number is made interesting by that fact. For example, if 39 and 46 were the first two uninteresting numbers, then 39 would become interesting as a result, but 46 would not since it is not the first uninteresting number." There seems to be an obvious flaw here. If 39 becomes interesting, it is no longer an uninteresting number, so it can't be the lowest uninteresting number; 46 would be the new smallest uninteresting number. 208.54.70.130 (talk) 02:07, 17 June 2015 (UTC)

Bellos' definition
Just a quick note that, using Alex Bellos' (probably humorous) definition of "the lowest number not to have its own page on Wikipedia", the lowest uninteresting number is 1002. And it's not just uninteresting by chance; it's uninteresting by consensus. Howicus (Did I mess up?) 01:18, 14 March 2016 (UTC)
 * I was wrong, 247 is still a redirect. Howicus (Did I mess up?) 01:23, 14 March 2016 (UTC)

17843 is a Semi-uninteresting Number
I noticed that this Wikipedia page is out of date because 14972 appears as the seventh entry in a sequence so is no longer uninteresting. Searching forward from 14972, I found no uninteresting numbers until 17843. Look up http://oeis.org/search?q=17843. 17843 does appear in the OEIS, but does not appear in a integer sequence in the OEIS. It appears only as the 35th coefficient of an empirical approximation to the sequence. Does that make it interesting? Or uninteresting? Or both? Mollwollfumble (talk) 19:05, 18 November 2016 (UTC)

What makes a number interesting?
I don't see an actual method for determining this given anywhere in the article; and the definitions that are offered have no reasoning supporting them. — Preceding unsigned comment added by 98.219.84.14 (talk) 21:59, 24 December 2020 (UTC)

Nominated for deletion
This page has been nominated for deletion at Articles for deletion/Interesting number paradox (2nd nomination), possibly to make it the most interesting paradox without a Wikipedia article. Certes (talk) 21:25, 13 October 2022 (UTC)

Possible Citation sources to make article better?
Some sources cited in defence on the AfD page, just putting them here so they don't get lost, no idea as to the quality

Chaitin also calls attention to its relation to an earlier paradox of Russell on the existence of a smallest undefinable ordinal (despite the fact that all sets of ordinals have a smallest element and that "the smallest undefinable ordinal" would appear to be a definition):

All on JSTOR... obviously a paywall does not stop them being valid, just anyone on the outside from using them to improve the article.

82.22.50.11 (talk) 23:41, 13 October 2022 (UTC)

39 is really interesting!
39 is interesting since it is the smallest number > 2 such that the Mertens function return 0 (see, I really don’t know why David Wells thought that it is uninteresting, also see , all natural numbers up to 80 are really interesting, the next number 81 is 3^4 thus no reason to be uninteresting, but for 82 (why 82 is interesting? Companion Pell number? Number of 6-hexes? Squarefree semiprime? Ulam number? (Only mathematics-related properties are allowed, and only base-independent properties are allowed, thus you cannot say that 82 is interesting because it is the largest atomic number of a stable isotope, and you cannot say that 82 is interesting because its multiplicative inverse has only period length 5 in decimal)) 61.224.145.154 (talk) 06:31, 22 August 2023 (UTC)