smallest unused natural number

[Danijel Gorupec]

Stupid, but still interests me

 

I define that a number is 'used' if at least once in history at least one human being ever used it in any way (write, read, tell or even think of), the question is 'what is the order of magnitude of the smallest never-used natural number'?

 

Note1: numbers that are never used as numbers, but instead as array of digits, are not spent and are considered unused. For example, telephone numbers.

Note2: numbers used inside machines (computers) during computation procedures are not spent (except if a human being reviewed the process and noticed them).

Note3: just a brief look at a paper sheet full of numbers will not spend them all. To spend any you must actuall 'load it into your mind' as a number.

 

I know that there is no definite answer. I am just asking what is your best guess. My best guess is that the smallest unused natural is in 100-million range. Or can it be even smaller?

[uncool]

I think that it is 235962.

 

Oh. Never mind. Must be 235963.

=Uncool-

[Mr Skeptic]

Um, telephone numbers are actually rather important, and each phone number will usually be known by at least one person. And then there is social security numbers, driver's license numbers, bank account numbers, ... I think there might be some unused 10 digit numbers.

 

Actually, if you ask swansont, he probably has a number for each fraction of a second, and he's probably up to the 20 digit range already.

[Danijel Gorupec]

Well, I beleive peopole did count up to one million - even on loud. Probably there were freaks that counted up to ten million (at least in their heads). But above ten million, there might be unused numbers.

 

...

 

I beleive that peopole don't think about telephone numbers as integers. Instead they think about telephone numbers as array of digits. This is a different thing.

 

Thanks for your replies

 

 

 

 

[CaptainPanic]

I'm just trying to find a methodology here... (and failing to find it - but it may be a start).

 

So, as stated by the OP, we exclude bank accounts, phone numbers, bar codes, passport numbers, serial numbers of all kinds of products, project numbers, driver's licence numbers, and all other numbers that are just a row of digits, but don't necessarily represent the number

 

That leaves us with:

 

Distances

Industrial and agricultural production units

Other numbers used in sciences

Money

etc

 

Basically, we need:

- An estimate of how often a human being says a significantly large number in any category

- An estimate of how often that number is being rounded off, or has a decimal

 

We know we have about 7 billion people on earth, of which at least 2 billion will be educated enough to be able to handle numbers into the billions.

 

Then we can make a statistical analysis of the chance that there is an unused number below a certain value. (Nearly impossible, but hey, this isn't my idea or question)

 

As how to find the actual number... I fear we must install Big Brother first, and monitor every person in the world...

 

I hope you weren't asking a trick question where the answer is: "as soon as you find the number, it is used, and the answer (whatever answer) becomes invalid as soon as you find it"...

Edited August 31, 2010 by CaptainPanic

[John Cuthber]

I googled "1" and got lots of hits. Then I tried "2" and still got lots so, I think that the evidence shows the number is more than 2.

 

Imagine someone with better computing skills repeated that process automatically until they came to a number that wasn't used.

That would be the smallest number not on the (googleable) web.

If they posted the outcome here and google found it...

[Danijel Gorupec]

I googled "1" and got lots of hits. Then I tried "2" and still got lots so, I think that the evidence shows the number is more than 2.

 

Imagine someone with better computing skills repeated that process automatically until they came to a number that wasn't used.

That would be the smallest number not on the (googleable) web.

If they posted the outcome here and google found it...

 

Impressed with your method! (Of course, the programmer of such algorithm will have to find a way to reject phone numbers and other digit-trains). But this could be the doable method to estimate the order of magnitude of the smallest never used natural number.

 

I hope you weren't asking a trick question where the answer is: "as soon as you find the number, it is used, and the answer (whatever answer) becomes invalid as soon as you find it"...

 

I have no answer. The question is open. I am happy to hear your personal estimates (for order of magnitude). And I am even happier to hear about methods that can be used to 'calculate' its order of magnitude. Thanks.

[ajb]

It is an interesting question. I too have no real clue what the answer is.

 

Just for fun, let me throw a few numbers into the mix.

 

number of cells in the human body [math]> 10^{14}[/math].

 

Avagadro's constant (number of atoms/molecules per mole) [math]6 \times 10^{23}[/math].

 

Number of stars in the observable universe [math]5 \times 10^{22}[/math].

 

Estimate of the number of fundamental particles in the observable universe [math] \approx 10^{80}[/math].

 

Numbers like [math]10^{100}[/math]~ [math]10^{500}[/math] are quoted for the number of operations needed in some deciphering problems. These are the biggest numbers I know.