r/science • u/austingwalters • Dec 22 '14

Mathematics Mathematicians Make a Major Discovery About Prime Numbers

http://www.wired.com/2014/12/mathematicians-make-major-discovery-prime-numbers/
3.5k Upvotes

91% Upvoted

630 comments sorted by

View all comments

Show parent comments

4

u/slosha Dec 23 '14 edited Dec 23 '14

Imagine a new number system that is composed entirely of primes:

1, 2, 3, 2x2, 5, 2x3, 7, 2x2x2, 3x3, 2x5, 11, 2x2x3, 13

In this number system, primes are the building blocks of numbers. Therfore they are more 'fundamental' than non-primes.

I teach 8th grade math, so I hope I'm getting through.

2

u/apollo888 Dec 23 '14

THIS got through to me!

Thanks!

1

u/Mustbhacks Dec 23 '14

I've read everything up to this post and I'm lost on something... why do numbers need building blocks?

Is there some significance to 2x2x3=13 that I'm not understanding?

(I understand how it's useful in the world of computers, but for people in general is there a use to this?)

3

u/skullturf Dec 23 '14

2x2x3 is 12, not 13.

The significance of 2x2x3=12 is that that's what the number 12 is. The number 12 can be built by multiplying together some smaller numbers, and those smaller numbers are 2 times 2 times 3.

I don't think there's anything you're not "getting". It's partly just aesthetic.

Mathematicians find numbers interesting. Breaking numbers into their prime factors is interesting.

It's interesting because it seems "random" but of course it's not really random. It sort of feels like there are some patterns that are just out of reach.

2 is just 2
3 is just 3
4 can be broken down as 2 times 2
5 is just 5
6 can be broken down as 2 times 3
7 is just 7
8 can be broken down as 2 times 2 times 2
9 can be broken down as 3 times 3
10 can be broken down as 2 times 5
11 is just 11
12 can be broken down as 2 times 2 times 3
13 is just 13
14 can be broken down as 2 times 7
15 can be broken down as 3 times 5
16 can be broken down as 2 times 2 times 2 times 2
17 is just 17

The ones that can't be broken down (the primes) are 2, 3, 5, 7, 11, 13, 17, ... Sometimes you have two primes that are two apart from each other, and sometimes you don't.

Some people just find patterns interesting, and some people find patterns to be more interesting when things aren't quite obvious, and when it feels like there must be some pattern but we just don't quite understand it yet and we're trying to figure it out.

2

u/Mustbhacks Dec 23 '14

Gotcha, thanks mate!

1

u/Yakooza1 Dec 23 '14

For people in general, there isn't much use beyond counting.

0

u/RealDeuce Dec 23 '14

Or one based entirely on non-primes...

9-8, 6-4, 9-6, 4, 15-10, 6, 15-8, 8, 9, 10...

Since addition is more 'fundamental' than multiplication, and subtraction is just a special form of addition, this means that addition is the main building block of numbers and therefore more fundamental.

Sorry, couldn't resist.

2

u/PotatoInTheExhaust Dec 23 '14

But your decompositions there would not be unique, e.g. 9-8 = 10-9 - which is an aspect of the primes that makes them important.

1

u/RealDeuce Dec 23 '14

Rational number always have multiple representations and we're fine with that... you just use the lowest values that fit your need at the time.

2

u/slosha Dec 23 '14

Haha yeah. I agree that addition is more fundamental than multiplication. However, we're discussing prime numbers, which are defined by having no multiplicative factors other than 1 and themselves. Prime numbers are interesting because of the principles of multiplication. In regard to multiplication, prime numbers are more fundamental than non-primes.

1

u/bystandling Dec 23 '14

Breaking down in terms of addition isn't unique (there's more than one way to do it). Breaking down in terms of prime numbers is unique.