# Can you make any integer sound impressive and important? **URL:** \ **Category:** Factual Questions\ **Created:** [November 14, 2012, 11:03am UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970 "2012-11-14T11:03:04Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Jragon](https://avatars.discourse-cdn.com/v4/letter/j/e19b73/32.png) [@Jragon](https://boards.straightdope.com/u/Jragon)\ **Post date:** [November 14, 2012, 11:03am UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/1 "2012-11-14T11:03:04Z")
I’m just curious if it’s common for numbers to have a ton of arbitrary mathematical properties. 42, for instance, seems to have a laundry list of not-really-bizarre-but-kind-of-cool mathematical properties. Often with impressive sounding names like “pronic number” (product of two successive integers). But I really wonder, if I picked a random integer, could a sufficiently bored mathematician find a comprehensive list of a bunch of impressive sounding but relatively meaningless properties? It seems like you could, but I have heard some say things like how certain important numbers (like 666) are actually “really boring” mathematically. However, even if some numbers are “boring” can you get a bunch of impressive sounding properties for most of them (yes, I realize the futility of asking this question about an infinite set)? I suspect non-primes are going to fare better than primes in this department, simply because being prime excludes you from a whole class of properties involving your factors, but who knows, they may make up for it in other ways. ---
**Author:** ![drewtwo99](https://avatars.discourse-cdn.com/v4/letter/d/d07c76/32.png) [@drewtwo99](https://boards.straightdope.com/u/drewtwo99)\ **Post date:** [November 14, 2012, 11:15am UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/2 "2012-11-14T11:15:11Z")
Claim: There is no such thing as an uninteresting natural number. Proof by Contradiction: Assume that there is a non-empty set of natural numbers that are not interesting. Due to the well-ordered property of the natural numbers, there must be some smallest number in the set of uninteresting numbers. Being the smallest number of a set one may consider uninteresting makes that number interesting after all: a contradiction. (Source: Wikipedia) ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [November 14, 2012, 11:56am UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/3 "2012-11-14T11:56:15Z")
Hmm. I’ve never found that proof all that convincing; it smacks of the unexpected hanging paradox to me. But I guess that what we mean by interesting number is not a clear concept anyway, so it’s moot. ---
**Author:** ![Noone\_Special](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/noone_special/32/2863_2.png) [@Noone\_Special](https://boards.straightdope.com/u/Noone_Special)\ **Post date:** [November 14, 2012, 12:12pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/4 "2012-11-14T12:12:53Z")
> [@Mijin](#): > > Hmm. I’ve never found that proof all that convincing; it smacks of the unexpected hanging paradox to me. > But I guess that what we mean by interesting number is not a clear concept anyway, so it’s moot. Which makes it pretty much **exactly** the same as the “unexpected hanging” paradox – since that one essentially hinges on the unclearness of what “unexpected” means. ---
**Author:** ![njtt](https://avatars.discourse-cdn.com/v4/letter/n/ecd19e/32.png) [@njtt](https://boards.straightdope.com/u/njtt)\ **Post date:** [November 14, 2012, 12:40pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/5 "2012-11-14T12:40:27Z")
**[FONT=“Impact”]137**[/FONT] ---
**Author:** ![JKellyMap](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jkellymap/32/15880_2.png) [@JKellyMap](https://boards.straightdope.com/u/JKellyMap)\ **Post date:** [November 14, 2012, 12:46pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/6 "2012-11-14T12:46:06Z")
You can if you \*sing \*it. “8675309…”…oh, and what was that Police song? 😉 ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [November 14, 2012, 1:11pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/7 "2012-11-14T13:11:08Z")
There are people who really do get devoted to finding out, listing, and remembering the facts about numbers. Case in point, one of my favorite math books, the _Penguin Dictionary of Curious and Interesting Numbers_: > **[The Penguin Book of Curious and Interesting Numbers: Revised Edition: Wells,...](https://www.amazon.com/Penguin-Book-Curious-Interesting-Numbers/dp/0140261494)** > > Buy The Penguin Book of Curious and Interesting Numbers: Revised Edition on Amazon.com ✓ FREE SHIPPING on qualified orders Second case in point, the story of G.H. Hardy and Srinivasa Ramanujan: > [@](#): > > “ > > I remember once going to see him when he was ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavorable omen. “No,” he replied, “it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” > **[1729 (number)](https://en.wikipedia.org/wiki/1729_(anecdote))** > > 1729 is the natural number following 1728 and preceding 1730. It is the first nontrivial taxicab number, expressed as the sum of two cubic numbers in two different ways. It is known as the Ramanujan number or Hardy–Ramanujan number after G. H. Hardy and Srinivasa Ramanujan. > 1729 is composite, the squarefree product of three prime numbers 7 × 13 × 19. It has as factors 1, 7, 13, 19, 91, 133, 247, and 1729. It is the third Carmichael number, and the first Chernick–Carmichael number.\[a\] Furthermor... ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [November 14, 2012, 1:15pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/8 "2012-11-14T13:15:17Z")
Further down on that page is a relevant quote. I’d heard it before, but forgot it until I just re-read it: > [@](#): > > “Every positive integer is one of Ramanujan’s personal friends.”—J. E. Littlewood, upon hearing of the taxicab incident.[6] ---
**Author:** ![K364](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/k364/32/5_2.png) [@K364](https://boards.straightdope.com/u/K364)\ **Post date:** [November 14, 2012, 1:48pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/9 "2012-11-14T13:48:26Z")
73 is the best number [according to Sheldon Cooper](http://en.wikipedia.org/wiki/73_(number)#In_popular_culture) ---
**Author:** ![billfish678](https://avatars.discourse-cdn.com/v4/letter/b/7bcc69/32.png) [@billfish678](https://boards.straightdope.com/u/billfish678)\ **Post date:** [November 14, 2012, 1:55pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/10 "2012-11-14T13:55:51Z")
> [@Jragon](#): > > I suspect non-primes are going to fare better than primes in this department, simply because being prime excludes you from a whole class of properties involving your factors, but who knows, they may make up for it in other ways. So, some numbers are like the pretty girls and some are like the girls with a nice personality? 🙂 ---
**Author:** ![Kamino\_Neko](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kamino_neko/32/34_2.png) [@Kamino\_Neko](https://boards.straightdope.com/u/Kamino_Neko)\ **Post date:** [November 14, 2012, 2:00pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/11 "2012-11-14T14:00:03Z")
> [@](#): > > Masahiko Fujiwara showed that 1729 is one of four positive integers (with the others being 81, 1458, and the trivial case 1) which, when its digits are added together, produces a sum which, when multiplied by its reversal, yields the original number: Mathematicians are so adorable! ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [November 14, 2012, 2:05pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/12 "2012-11-14T14:05:37Z")
91 has two interesting properties. It is the smallest positive integers that is the sum of two cubes in two different ways. And it is smallest composite number that most people think is prime. ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [November 14, 2012, 2:06pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/13 "2012-11-14T14:06:44Z")
> [@Kamino\_Neko](#): > > Mathematicians are so adorable! I remember reading that taxicab 1729 anecdote and thinking, “Seriously?” I thought some of my friends were geeky but couldn’t imagine any of them complaining to an ill friend in hospital that the number of their cab was “dull”! ---
**Author:** ![WhyNot](https://avatars.discourse-cdn.com/v4/letter/w/c77e96/32.png) [@WhyNot](https://boards.straightdope.com/u/WhyNot)\ **Post date:** [November 14, 2012, 2:11pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/14 "2012-11-14T14:11:38Z")
This is oozing into the metaphysical, but the Kabbalistic (new age version, don’t know about orthodox version) of reality is that ANYTHING can, and should, be connected to something else in an interesting way. Numbers, words, people, objects, concepts, this pen, that tree…connect everything there is to connect, and the last things left to connect are you and YHVH (God.) … Dude, who’s got the Doritos? 😛 ---
**Author:** ![Mijin](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mijin/32/9369_2.png) [@Mijin](https://boards.straightdope.com/u/Mijin)\ **Post date:** [November 14, 2012, 2:11pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/15 "2012-11-14T14:11:40Z")
> [@Colophon](#): > > I remember reading that taxicab 1729 anecdote and thinking, “Seriously?” I thought some of my friends were geeky but couldn’t imagine any of them complaining to an ill friend in hospital that the number of their cab was “dull”! Yep. By rights, having someone appear at Ramanujan’s bedside, with an observation like that, should have tipped him into a coma. ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [November 14, 2012, 2:29pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/16 "2012-11-14T14:29:48Z")
> [@njtt](#): > > **[FONT=“Impact”]137**[/FONT] It’s the smallest three-digit prime such that it remains prime if you omit any digit! ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [November 14, 2012, 2:37pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/17 "2012-11-14T14:37:10Z")
…wait, were you playing off that fine-structure constant thing? ---
**Author:** ![ZipperJJ](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/zipperjj/32/211_2.png) [@ZipperJJ](https://boards.straightdope.com/u/ZipperJJ)\ **Post date:** [November 14, 2012, 3:05pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/18 "2012-11-14T15:05:04Z")
> [@Half\_Man\_Half\_Wit](#): > > …wait, were you playing off that fine-structure constant thing? I think he was going for “looks impressive, all bold, centered and large like that.” ---
**Author:** ![j\_sum1](https://avatars.discourse-cdn.com/v4/letter/j/8baadc/32.png) [@j\_sum1](https://boards.straightdope.com/u/j_sum1)\ **Post date:** [November 14, 2012, 3:12pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/19 "2012-11-14T15:12:14Z")
> [@Hari\_Seldon](#): > > 91 has two interesting properties. It is the smallest positive integers that is the sum of two cubes in two different ways. And it is smallest composite number that most people think is prime. 4^3+3^3 What’s the other? ---
**Author:** ![Kamino\_Neko](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kamino_neko/32/34_2.png) [@Kamino\_Neko](https://boards.straightdope.com/u/Kamino_Neko)\ **Post date:** [November 14, 2012, 3:17pm UTC](https://boards.straightdope.com/t/can-you-make-any-integer-sound-impressive-and-important/640970/20 "2012-11-14T15:17:56Z")
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