# Are there any numbers still left to be invented or discovered. **URL:** \ **Category:** Factual Questions\ **Created:** [August 8, 2016, 9:44pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193 "2016-08-08T21:44:28Z")\ **Posts on this page:** 13\ **Page:** 3
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [August 9, 2016, 3:32pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/41 "2016-08-09T15:32:35Z")
Speaking of which, every so often someone discovers a new prime number (often a Mersenne prime). We’ve known for a very long time that there are infinitely many prime numbers (there is no Largest Prime Ever), but at any given time, there’s a largest _known_ prime number, and it’s big news when a larger one than that is discovered. ---
**Author:** ![Boyo\_Jim](https://avatars.discourse-cdn.com/v4/letter/b/87869e/32.png) [@Boyo\_Jim](https://boards.straightdope.com/u/Boyo_Jim)\ **Post date:** [August 9, 2016, 6:14pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/42 "2016-08-09T18:14:07Z")
For a time, there was the little known number [of wisserteen](http://boards.straightdope.com/sdmb/showpost.php?p=15414132&postcount=9). But the [number was eliminated](http://boards.straightdope.com/sdmb/showpost.php?p=15484611&postcount=184) in 2012 as being too divisive. ---
**Author:** ![Atamasama](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/atamasama/32/12961_2.png) [@Atamasama](https://boards.straightdope.com/u/Atamasama)\ **Post date:** [August 9, 2016, 8:41pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/43 "2016-08-09T20:41:16Z")
> [@jtur88](#): > > Answering that question would be self-defeating, since the post revealing that number would become a google hit. Now I’m tempted to request an example of something that will never be posted on this message board. ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [August 9, 2016, 8:58pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/44 "2016-08-09T20:58:33Z")
> [@jtur88](#): > > Answering that question would be self-defeating, since the post revealing that number would become a google hit. Well, one could be clever about it, and say something like “the number you get by adding 1 to 100130211006 has no google hits”. But I’m sure some joker here is going to ruin it by replying with the number in their post. –Mark ---
**Author:** ![Colophon](https://avatars.discourse-cdn.com/v4/letter/c/f05b48/32.png) [@Colophon](https://boards.straightdope.com/u/Colophon)\ **Post date:** [August 9, 2016, 9:38pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/45 "2016-08-09T21:38:12Z")
> [@Riemann](#): > > So, what’s the smallest integer with no Google hits? There’s a page with something to do with yoga in the URL that has a long list of integers. But it doesn’t have 92615000000 + 2. And I’m not bored enough to find any smaller. ---
**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\ **Post date:** [August 10, 2016, 2:31am UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/46 "2016-08-10T02:31:28Z")
> [@Thudlow\_Boink](#): > > Before that, everybody always had at least one of everything. 🙂 > > The OP’s is an ill-defined question, and there are a number (heh) of ways of thinking about it. > > There are “special numbers,” like pi and e and phi, that were at some point “discovered” in the sense that someone was the first to realize that there was something special about them—that they had some remarkable property. There are presumably other such numbers that have yet to be “discovered” in this way. > > There are unresolved questions in mathematics and science whose answer would be a number. In some cases it might even be a number that has never been “used” or referred to before by human beings. > > There are number _systems_ (e.g. Cantor’s (transfinite) cardinal numbers, quaternions, surreal numbers) that have been invented or discovered (depending on your point of view), and there’s no reason to think that others might be invented/discovered in the future. Indeed, since real numbers were algebraically extended to complex numbers, which in turn were generalized into the quaternions, and even those broadened into the [octonions](https://en.wikipedia.org/wiki/Octonion), I keep wondering if/when someone will devise a logically consistent system of hexadecions. (Unless we know that’s not possible). ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [August 10, 2016, 2:42am UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/47 "2016-08-10T02:42:30Z")
> [@Lumpy](#): > > Indeed, since real numbers were algebraically extended to complex numbers, which in turn were generalized into the quaternions, and even those broadened into the [octonions](https://en.wikipedia.org/wiki/Octonion), I keep wondering if/when someone will devise a logically consistent system of hexadecions. (Unless we know that’s not possible). It’s not possible. The octonions are as far as it goes. ---
**Author:** ![Hellestal](https://avatars.discourse-cdn.com/v4/letter/h/3ab097/32.png) [@Hellestal](https://boards.straightdope.com/u/Hellestal)\ **Post date:** [August 10, 2016, 5:33am UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/48 "2016-08-10T05:33:37Z")
> [@Lumpy](#): > > Indeed, since real numbers were algebraically extended to complex numbers, which in turn were generalized into the quaternions, and even those broadened into the [octonions](https://en.wikipedia.org/wiki/Octonion), I keep wondering if/when someone will devise a logically consistent system of hexadecions. (Unless we know that’s not possible). [Sedenions](https://en.wikipedia.org/wiki/Sedenion) But you lose properties the further up you go. The octonions aren’t associative, but are [alternative](https://en.wikipedia.org/wiki/Alternative_algebra). The sedenions aren’t even alternative. ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [August 10, 2016, 7:09am UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/49 "2016-08-10T07:09:57Z")
There are remarkable numbers still turning up. Numberphile makes a big deal out of Mill’s constant, A = 1.3063778838630806904686144926… with the property that ⌊ A[sup]3[sup]n[/sup][/sup]⌋ is prime for _all_ natural numbers n. However, there are infinitely many real numbers A with that property. I think the prime-generation capability of Euler’s lucky number 41 is more impressive (n[sup]2[/sup] + n + 41 is prime for all natural n \< 40). Particularly impressive is the way Euler’s lucky number leads to Martin Gardner’s April Fool’s Integer e[sup]π√(4\*41-1)[/sup] = 262537412640768743.999999999999… ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [August 10, 2016, 9:13am UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/50 "2016-08-10T09:13:52Z")
> [@septimus](#): > > Particularly impressive is the way Euler’s lucky number leads to Martin Gardner’s April Fool’s Integer (M) > M = e[sup]π√(4\*41-1)[/sup] = 262537412640768743.999999999999250… Playing around just now, I squared the April Fool’s Integer (M) to get M[sup]2[/sup] = 68925893036109279891085639286943768.0000000001637… At first I expected a number with fractional part .999… but of course the reciprocal of M is much smaller than its difference from an integer so that didn’t make sense. But why does M[sup]2[/sup] have fractional part .0000000001… ? The odds of a random real being so close to an integer are less than one in a billion. Coincidence? I doubt it: I checked another Heegner number ( e[sup]π√(4\*17-1)[/sup]) and see a similar result. Is this a well-known result? I shan’t play on **Indistinguishable** ’s patience since I’d be at a loss just to explain the closeness of the April Fool’s result itself. :o ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [August 10, 2016, 1:59pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/51 "2016-08-10T13:59:08Z")
[(pdf) Here’s one mathematician’s list of the ten “coolest” numbers.](http://homepages.umflint.edu/~mclemanc/Files/McLemanCoolestNumbers.pdf) He has the Heegner number 163 in the #1 slot. I was intrigued by his #8, a _Sierpinski number_: Upthread was a formula that generates only prime numbers when n is a natural number, but (using a Sierpinski number) the formula 78557\*2[sup]n[/sup] + 1generates only composites! ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [August 10, 2016, 3:20pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/52 "2016-08-10T15:20:33Z")
> [@septimus](#): > > Playing around just now, I squared the April Fool’s Integer (M) to get M[sup]2[/sup] = 68925893036109279891085639286943768.0000000001637… I think that’s a flaw in whatever tool you used to do the calculation. 262537412640768743.999999999999250 squared is 68925893036109279891085639286943729.8810388468840000000000… Your answer differs after 33 digits. –Mark ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [August 10, 2016, 3:52pm UTC](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193/53 "2016-08-10T15:52:51Z")
> [@markn\_1](#): > > I think that’s a flaw in whatever tool you used to do the calculation. > 262537412640768743.999999999999250 squared is > 68925893036109279891085639286943729.8810388468840000000000… > > Your answer differs after 33 digits. > > –Mark The number I’ve underlined above is _not_ the exact number. (I wrote “…”). If you have a tool good enough to multiply such precise numbers, it can probably produce a preciser approximation to e[sup]π√(4\*41-1)[/sup] = 262537412640768743.9999999999992500725971981856888793538563373369908627… BTW, not only is the square of this number very close to an integer, but so are all of its small powers, as well as its cube root. [Previous page](https://boards.straightdope.com/t/are-there-any-numbers-still-left-to-be-invented-or-discovered/762193.md?page=2)