Count To The First Insignificant Number!

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Vytron
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Count To The First Insignificant Number!

Postby Vytron » Mon Dec 08, 2014 5:52 am UTC

There's a theory that says all numbers are interesting, by the following reasoning:

1- There's a number n, so that n is uninteresting.

2- There's a number x, that has the above property, such that no number less than x has that property.

3- By 1 and 2, it follows that you can build a set of all numbers n, and it should include x.

4- x is interesting by being the very first member of this set.

5- By 2 and 4, x is both uninteresting and interesting.

6- By contradiction, 1 is proven false, because if there can't be a first number x that is uninteresting, that means all numbers are interesting.

Okay, perhaps that's true, so lets define Insignificance instead!

a) An Insignificant Number is one such that, all interesting properties that it may have, were already had by a previous number or more.

And that's it! Find me 2 uninteresting numbers, and the second one will be Insignificant, because being first on the uninteresting set was already taken, and being second is not significant!

So in this thread we count to THAT number! And from what I've seen, perhaps that number is below 100!

We also need to put a boundary on significance, which is:

b) The significance of a number should not be arbitrary.

That is, imagine 24. You might think it's significant because there's 24 hours in a day... think again! Would the world still be what it's today if we divided it in 12 double hours or 25 hours or whatever instead of 24? Yes, it would, so 24 can't be significant for this reason!

So, before counting, you need to give a good reason for significance, which is nontrivial.

And...

c) All Significant Numbers should be whole numbers.

In this thread we count 0, 1, 2, 3 (unless 1 is Insignificant and we're done already), and no number can be skipped.

I may add new rules here later, new rules will take effect retroactively, please be ready to edit your posts to comply with the last rules of the thread.

I'll start with:

0

Significance: The only number that can be used to state absence of something.

Next is 1, can you find significance in 1?

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Re: Count To The First Insignificant Number!

Postby azule » Mon Dec 08, 2014 9:05 am UTC

1, the only number, where in English, the object is singular. Even zero is plural.

Zero molpies.
One molpy.
Two molpies.

Even, 1.2 molpies.

That right, Vytron?
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Re: Count To The First Insignificant Number!

Postby orangedragonfire » Mon Dec 08, 2014 9:14 am UTC

2 is interesting because it's a prime number.

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Re: Count To The First Insignificant Number!

Postby Vytron » Mon Dec 08, 2014 9:25 am UTC

azule wrote:That right, Vytron?


Righty so! :)

And so, now, all numbers that can measure absence of quantity, can be used to name singular objects, or are only divisible by themselves or 1 are out! (no more primes)

3 is the noblest of all digits, as it is the only number to equal the sum of all the terms below it!

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Re: Count To The First Insignificant Number!

Postby azule » Mon Dec 08, 2014 10:48 am UTC

4 is the sum of 2+2 and the product of 2x2, and maybe some others that involve 2 2s.
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Re: Count To The First Insignificant Number!

Postby Vytron » Mon Dec 08, 2014 11:21 am UTC

5 is the first Safe Prime. A safe prime is a prime constructed by multiplying another prime by 2, and adding 1.

And now all other safe primes are insignificant! (or, er, they have to be significant for another reason)

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Re: Count To The First Insignificant Number!

Postby Lawrencelot » Mon Dec 08, 2014 12:58 pm UTC

6 is the first number that can be divided by multiple numbers (can be divided by 2 and by 3)

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Re: Count To The First Insignificant Number!

Postby Vytron » Mon Dec 08, 2014 1:15 pm UTC

7 is the lowest natural number that cannot be represented as the sum of the squares of three integers.

02+02+02=0

02+02+12=1

02+12+12=2

12+12+12=3

02+02+22=4

02+12+22=5

12+12+22=6

02+22+22=8

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Re: Count To The First Insignificant Number!

Postby Lunch Meat » Mon Dec 08, 2014 2:06 pm UTC

8 is the first cube of a prime number.

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Re: Count To The First Insignificant Number!

Postby Reecer6 » Mon Dec 08, 2014 2:09 pm UTC

9 is the first odd composite! 1 isn't prime, but it isn't composite either.

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Re: Count To The First Insignificant Number!

Postby ramblinjd » Mon Dec 08, 2014 2:30 pm UTC

10 is the first number in our agreed-upon counting system that uses two digits.
Spoiler:
If that doesn't have enough significance, then it is also the smallest noncototient, a number that cannot be expressed as the difference between any integer and the total number of coprimes below it.

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Re: Count To The First Insignificant Number!

Postby phillip1882 » Mon Dec 08, 2014 3:39 pm UTC

11 is the first prime number that can be expressed as the sum of three odd primes. 3+3+5
good luck have fun

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Re: Count To The First Insignificant Number!

Postby Vytron » Mon Dec 08, 2014 4:49 pm UTC

ramblinjd wrote:10 is the first number in our agreed-upon counting system that uses two digits.


That's fine but then that'd be "uses more than one digit", so 100, 1000, 10000... wouldn't be able to use the same system to become significant.

12 is a superior highly composite number because it has more divisors than any other number scaled relative to the number itself.

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Re: Count To The First Insignificant Number!

Postby Lunch Meat » Mon Dec 08, 2014 4:55 pm UTC

13 is the first prime that can be expressed as the sum of two squares of prime numbers.

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Re: Count To The First Insignificant Number!

Postby Vytron » Mon Dec 08, 2014 5:10 pm UTC

14 is the first nontotient.

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Re: Count To The First Insignificant Number!

Postby ramblinjd » Mon Dec 08, 2014 5:54 pm UTC

15 is the first non-perfect-square that is the product of two odd primes. (3*5 = 15).

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Re: Count To The First Insignificant Number!

Postby Lunch Meat » Mon Dec 08, 2014 6:16 pm UTC

16 is the first square of a square that is not the same as its square root.

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Re: Count To The First Insignificant Number!

Postby ramblinjd » Mon Dec 08, 2014 8:22 pm UTC

17 is the only prime positive Genocchi number.

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Re: Count To The First Insignificant Number!

Postby orangedragonfire » Mon Dec 08, 2014 9:12 pm UTC

18 is the first even number that is divisible by the square of an odd prime number.

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Re: Count To The First Insignificant Number!

Postby Vytron » Tue Dec 09, 2014 3:59 am UTC

19 - The only non-trivial normal magic hexagon contains 19 hexagons (the other being 1).

I already made the full explanation of what does it mean.

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Re: Count To The First Insignificant Number!

Postby cyanyoshi » Tue Dec 09, 2014 1:02 pm UTC

20 - is a primitive abundant number. If you add together all of its proper divisors {1,2,4,5,10}, you get something greater than 20. However, each proper divosor is a deficient number. For example, the proper divisors of 10 are {1,2,5}, which add up to be less than 10.

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Re: Count To The First Insignificant Number!

Postby cyanyoshi » Tue Dec 09, 2014 1:02 pm UTC

20 - is a primitive abundant number. If you add together all of its proper divisors {1,2,4,5,10}, you get something greater than 20. However, each proper divosor is a deficient number. For example, the proper divisors of 10 are {1,2,5}, which add up to be less than 10.

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Re: Count To The First Insignificant Number!

Postby cyanyoshi » Tue Dec 09, 2014 1:02 pm UTC

Oops, I posted twice for some reason. Guess I'll reserve 21.
...actually, never mind.
Last edited by cyanyoshi on Tue Dec 09, 2014 1:07 pm UTC, edited 2 times in total.

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Re: Count To The First Insignificant Number!

Postby Vytron » Tue Dec 09, 2014 1:05 pm UTC

That sounds...

Primitive.

Spoiler:
*shot*


21 - The smallest natural number that is not close to a power of 2, 2n, where the range of closeness is ±n.

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Re: Count To The First Insignificant Number!

Postby cyanyoshi » Wed Dec 10, 2014 12:05 am UTC

22 is the smallest number that can be written three different ways as the sum of two primes.
23 is the smallest prime number that isn't a twin prime.
24 is the only nontrivial solution to the cannonball problem (i.e. 12 + 22 + 32 + ... + 242 is a perfect square).

I don't understand what the heck happened with those posts. That last post was supposed to be an edit on the one before it...

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Re: Count To The First Insignificant Number!

Postby orangedragonfire » Wed Dec 10, 2014 12:14 am UTC

25 is the first square that is the sum of two other squares.

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Re: Count To The First Insignificant Number!

Postby azule » Wed Dec 10, 2014 2:33 am UTC

Math fails me. what are those numbers?

Nm, they're 3 and 4
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Re: Count To The First Insignificant Number!

Postby Vytron » Wed Dec 10, 2014 7:18 am UTC

26 - 26 is the only integer that is one greater than a square (52) and less than a cube (33)

The only integer! That's more significant than being the first member of a set!

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Re: Count To The First Insignificant Number!

Postby ramblinjd » Mon Dec 15, 2014 2:33 pm UTC

27 is the smallest odd cube (that isn't the same as its cubed root)
28 is the number of possible convex uniform honeycombs

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Re: Count To The First Insignificant Number!

Postby Vytron » Wed Dec 17, 2014 11:41 pm UTC

29 turned out to be pretty hard, I wonder if the first insignificant number is close!

29 - The first prime that is also a tetranacci number.

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Re: Count To The First Insignificant Number!

Postby Lunch Meat » Thu Dec 18, 2014 12:57 am UTC

30 is the first number that is equal to both a cube plus its cube root and a square plus its square root (where the numbers and roots are not the same number). (It might be the only number with this property, but I'm not sure how to prove it.)

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Re: Count To The First Insignificant Number!

Postby Vytron » Thu Dec 18, 2014 1:31 am UTC

31 has several things going on that make it unique, all cool. But let's go with:

31 is the first number that is a centered surrounded triangular number, surrounded centered pentagonal number AND surrounded centered decagonal number. (Added the "surrounded" part because otherwise 1 is all the first "n"ular number up to infinity, which would suck - but 1 is not surrounded)

(As with 30, It might be the only number with this property, but I'm not sure how to prove it.)

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Re: Count To The First Insignificant Number!

Postby Reecer6 » Thu Dec 18, 2014 2:20 am UTC

I'll take the easy 32, which is special for being the first fifth power (that isn't the same as its root).

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Re: Count To The First Insignificant Number!

Postby Vytron » Thu Dec 18, 2014 2:40 am UTC

33 is the smallest sum of two positive different numbers, each of which raised to the fifth power: 1^5 + 2^5 = 33.
Last edited by Vytron on Thu Dec 18, 2014 4:01 am UTC, edited 1 time in total.

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Re: Count To The First Insignificant Number!

Postby Reecer6 » Thu Dec 18, 2014 3:48 am UTC

I'll contest that 2 is the real smallest sum of two positive fifth powers. 1^5 + 1^5.

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Re: Count To The First Insignificant Number!

Postby Vytron » Thu Dec 18, 2014 4:02 am UTC

Okay, added "different" (edited wikipedia article as well.)

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Re: Count To The First Insignificant Number!

Postby WarDaft » Thu Dec 18, 2014 4:15 am UTC

34 is the smallest number with the property that it and its neighbours have the same number of divisors.

Also, I hate to say this, but there are also no insignificant numbers either, by analogy to same proof as that there are no uninteresting numbers.
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Re: Count To The First Insignificant Number!

Postby orangedragonfire » Thu Dec 18, 2014 2:32 pm UTC

35 is the number of free hexominoes

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Re: Count To The First Insignificant Number!

Postby Vytron » Thu Dec 18, 2014 4:54 pm UTC

WarDaft wrote:Also, I hate to say this, but there are also no insignificant numbers either, by analogy to same proof as that there are no uninteresting numbers.


I have an specific number in mind, to which I couldn't find any significance about it, because all interesting things that it had were previously had by another number. I'm looking forward to see what someone can find significant about it, and it's not that far from here...

36 - The first surrounded Square Triangular number.

(Again, 0 and 1 are the first whatevers of everythingular numbers, but they're not surrounded)

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Re: Count To The First Insignificant Number!

Postby Lunch Meat » Thu Dec 18, 2014 6:26 pm UTC

37 is the first two-digit prime number whose digits are different non-consecutive prime numbers.


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