Prime Numbers Visualized!

http://www.sievesofchaos.com/

"Wherever you have only 2 circles intersecting the horizontal axis at their right quadrants, you have a prime number!"

Seems to be a new thing, it's not even on Google yet. You heard it here first.

it's basically a fancy sieve of erastothnes, but it sure is pretty

2nd video made me kind of dizzy

Nice pictures, but he's an engineer, and mathematically he seems very naive.

e.g. his Excel algorithm for finding primes:

  Quote

1.Input the number 1 into the first cell “A1” (first row and first column) and continue to the right with consecutive numbers.

2.Input the number 2 into the cell “B2” (second row and second column) and continue to the right with the number 2 at every 2 columns.

3.Input the number 3 into the cell “C3” ( third row and third column) and continue to the right with the number 3 at every 3 columns.

4.Continue the input of data for the numbers 4, 5, 6, etc...

5.Input a counter at the bottom of the spreadsheet that will show the number in the first row of that column when there are only 2 numbers in that entire column.

6.The numbers shown at the bottom of the spreadsheet will inevitably be prime numbers.

... all he is doing here is laying out the very definition of prime numbers in a very long-winded way on a spreadsheet. 'When there are only 2 numbers in the column' simply means the number is divisible by 1 (duh) and itself. Ditto for his circles. He has not discovered anything.

The fact that he thought he would get a million dollars for generating a prime over 1 billion, when really it needed to be over 1 billion digits, kindof shows that he's a bit of a novice here.

Cryptography needs a steady supply of huge primes, and loads of heavy maths has been done in this area. e.g. see http://en.wikipedia.org/wiki/Primality_test

His circles and spreadsheets are fisher-price in comparison.

And another thing:

  Quote

These Maps of Factors are intriguing because they visually tell us that Prime Numbers are geometrically chaotic in nature. The way the Map of Factors is developed is actually a simple recursion process for circles, but it produces a complex and astonishing image. An image that requires absolutely all circles up to “n/2” where “n” is the point we want to probe for factors. I believe this is what makes Prime Numbers so elusive! There are no defined initial conditions that give them away! Their initial conditions are dependent on where the number is located on the map, so for different numbers, initial conditions are also different. Prime Numbers seem to possess an uncertainty principle (sort of like particles in Quantum Mechanics) that only allows for their probing as far as our computing power permits.

This paragraph is bollocks, mathematically speaking. There are proper definitions for what defines a 'chaotic' system, and the distribution of primes is not chaotic. Having a very complicated or unfathomable pattern does not necessarily mean something is chaotic. Secondly, the fact that we need a lot of computing power to look for primes in no way makes it anything like the Quantum 'uncertainly principle'.

yeah mathematically it is not interesting at all. I don't think it makes it easier to "visualize" prime numbers this way either. it does looks nice, but all he's doing is lining up circles.

This reminded me of something a friend told me.

apparently there's some guy out there, a savant or something, that actually visualizes numbers as 3d shapes, and he can make sculptures of a number and recognize it later he can also know if a number is prime or not just by it's shape. anyway i don't know if this is true at all because my friend is a compulsive liar of sorts and i never bothered to ask for the name.

  On 12/13/2009 at 10:19 PM, kaini said:

it's basically a fancy sieve of erastothnes, but it sure is pretty

  On 12/13/2009 at 10:48 PM, zazen said:

e.g. his Excel algorithm for finding primes:

  Quote

1.Input the number 1 into the first cell “A1” (first row and first column) and continue to the right with consecutive numbers.

2.Input the number 2 into the cell “B2” (second row and second column) and continue to the right with the number 2 at every 2 columns.

3.Input the number 3 into the cell “C3” ( third row and third column) and continue to the right with the number 3 at every 3 columns.

4.Continue the input of data for the numbers 4, 5, 6, etc...

5.Input a counter at the bottom of the spreadsheet that will show the number in the first row of that column when there are only 2 numbers in that entire column.

6.The numbers shown at the bottom of the spreadsheet will inevitably be prime numbers.

http://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

this one is interesting, but without pretty visuals

http://mathworld.wolfram.com/PrimeSpiral.html

you could make something pretty tho

  On 12/13/2009 at 11:13 PM, GORDO said:

This reminded me of something a friend told me.

 

apparently there's some guy out there, a savant or something, that actually visualizes numbers as 3d shapes, and he can make sculptures of a number and recognize it later he can also know if a number is prime or not just by it's shape. anyway i don't know if this is true at all because my friend is a compulsive liar of sorts and i never bothered to ask for the name.

maybe Daniel Tammet?

http://www.amazon.com/Born-Blue-Day-Extraordinary-Autistic/dp/1416535071

could be, i'll ask next time it comes up

Oooh pretty.

How much do they give you if you discover a new prime? I heard it was something good.

if you try and export it or someone is using it for something, they have been known to give you a spell in prison or at least a harsh talking-to by some agent smiths

http://en.wikipedia.org/wiki/Illegal_prime

Bummer.

Also it says the 1st illegal prime is 4

  On 12/14/2009 at 2:16 AM, chassis said:

Bummer.

 

Also it says the 1st illegal prime is 4

... no it's:

4 85650 78965 73978 29309 84189 46942 86137 70744 20873 51357 92401 96520 73668 69851 34010 47237 44696 87974 39926 11751 09737 77701 02744 75280 49058 83138 40375 49709 98790 96539 55227 01171 21570 25974 66699 32402 26834 59661 96060 34851 74249 77358 46851 88556 74570 25712 54749 99648 21941 84655 71008 41190 86259 71694 79707 99152 00486 67099 75923 59606 13207 25973 79799 36188 60631 69144 73588 30024 53369 72781 81391 47979 55513 39994 93948 82899 84691 78361 00182 59789 01031 60196 18350 34344 89568 70538 45208 53804 58424 15654 82488 93338 04747 58711 28339 59896 85223 25446 08408 97111 97712 76941 20795 86244 05471 61321 00500 64598 20176 96177 18094 78113 62200 27234 48272 24932 32595 47234 68800 29277 76497 90614 81298 40428 34572 01463 48968 54716 90823 54737 83566 19721 86224 96943 16227 16663 93905 54302 41564 73292 48552 48991 22573 94665 48627 14048 21171 38124 38821 77176 02984 12552 44647 44505 58346 28144 88335 63190 27253 19590 43928 38737 64073 91689 12579 24055 01562 08897 87163 37599 91078 87084 90815 90975 48019 28576 84519 88596 30532 38234 90558 09203 29996 03234 47114 07760 19847 16353 11617 13078 57608 48622 36370 28357 01049 61259 56818 46785 96533 31007 70179 91614 67447 25492 72833 48691 60006 47585 91746 27812 12690 07351 83092 41530 10630 28932 95665 84366 20008 00476 77896 79843 82090 79761 98594 93646 30938 05863 36721 46969 59750 27968 77120 57249 96666 98056 14533 82074 12031 59337 70309 94915 27469 18356 59376 21022 20068 12679 82734 45760 93802 03044 79122 77498 09179 55938 38712 10005 88766 68925 84487 00470 77255 24970 60444 65212 71304 04321 18261 01035 91186 47666 29638 58495 08744 84973 73476 86142 08805 29443

Ahh.

The way they have it written there seems very strange to me.

  On 12/14/2009 at 2:20 AM, Glass Plate said:

  On 12/14/2009 at 2:16 AM, chassis said:

Bummer.

 

Also it says the 1st illegal prime is 4

... no it's:

4 85650 78965 73978 29309 84189 46942 86137 70744 20873 51357 92401 96520 73668 69851 34010 47237 44696 87974 39926 11751 09737 77701 02744 75280 49058 83138 40375 49709 98790 96539 55227 01171 21570 25974 66699 32402 26834 59661 96060 34851 74249 77358 46851 88556 74570 25712 54749 99648 21941 84655 71008 41190 86259 71694 79707 99152 00486 67099 75923 59606 13207 25973 79799 36188 60631 69144 73588 30024 53369 72781 81391 47979 55513 39994 93948 82899 84691 78361 00182 59789 01031 60196 18350 34344 89568 70538 45208 53804 58424 15654 82488 93338 04747 58711 28339 59896 85223 25446 08408 97111 97712 76941 20795 86244 05471 61321 00500 64598 20176 96177 18094 78113 62200 27234 48272 24932 32595 47234 68800 29277 76497 90614 81298 40428 34572 01463 48968 54716 90823 54737 83566 19721 86224 96943 16227 16663 93905 54302 41564 73292 48552 48991 22573 94665 48627 14048 21171 38124 38821 77176 02984 12552 44647 44505 58346 28144 88335 63190 27253 19590 43928 38737 64073 91689 12579 24055 01562 08897 87163 37599 91078 87084 90815 90975 48019 28576 84519 88596 30532 38234 90558 09203 29996 03234 47114 07760 19847 16353 11617 13078 57608 48622 36370 28357 01049 61259 56818 46785 96533 31007 70179 91614 67447 25492 72833 48691 60006 47585 91746 27812 12690 07351 83092 41530 10630 28932 95665 84366 20008 00476 77896 79843 82090 79761 98594 93646 30938 05863 36721 46969 59750 27968 77120 57249 96666 98056 14533 82074 12031 59337 70309 94915 27469 18356 59376 21022 20068 12679 82734 45760 93802 03044 79122 77498 09179 55938 38712 10005 88766 68925 84487 00470 77255 24970 60444 65212 71304 04321 18261 01035 91186 47666 29638 58495 08744 84973 73476 86142 08805 29443

a crack team composed of an NSA agent, a CIA agent, and a member of the RIAA has been dispatched to your house.

please stay calm and remain in your chair in the basement eating cheetos.

edit: before you ask, have you seen the size of jimbo's ranch in texas?

Optimus is the first prime bitches

  On 12/14/2009 at 2:44 AM, Philip Glass said:

Optimus is the first prime bitches

But he's legal, at least he told me he was as he held me close.

number theory and graph theory were just about the only two parts of my mathematics degree that i didn't fail miserably at. that and fourier anaylsis.

but still, cracking the theory of primes is far beyond my comprehension. or i guess i'd be a multimillionaire.

  On 12/14/2009 at 2:51 AM, margaret thatcher said:

number theory and graph theory were just about the only two parts of my mathematics degree that i didn't fail miserably at. that and fourier anaylsis.

but still, cracking the theory of primes is far beyond my comprehension. or i guess i'd be a multimillionaire.

what really infuriates pure mathematicians is that despite the many theories and formulae which spit out primes at varying speeds (computationally speaking), we are incomplete - in the kurt godel sense. in other words we don't know if any theory - or even the sum of all our theories - will spit out every prime. worse again, we don't even know if they won't.

or to put it another way if you were to

1. take prime number N 2.take the distance between it and the next prime number, N+1 3. print the result 4. loop around and plug the result into N

it would be a completely irrational number like e or pi

  On 12/14/2009 at 2:51 AM, margaret thatcher said:

number theory and graph theory were just about the only two parts of my mathematics degree that i didn't fail miserably at. that and fourier anaylsis.but still, cracking the theory of primes is far beyond my comprehension. or i guess i'd be a multimillionaire.

I god dont remind me. I hope to god I scraped a pass for my Maths module. We did basic number theory, among other things.

when they introduce you to aleph infinites it's like getting past thethan level 3 in scientology. allegedly.

  On 12/14/2009 at 3:04 AM, kaini said:

what really infuriates pure mathematicians is that despite the many theories and formulae which spit out primes at varying speeds (computationally speaking), we are incomplete - in the kurt godel sense. in other words we don't know if any theory - or even the sum of all our theories - will spit out every prime. worse again, we don't even know if they won't.

I thought there was a simple formula for defining prime numbers, like doubling a prime and adding one. Or am I thinking of some other formula?

there are many, but none that can be proven to hold true for all values

otherwise crypto would be a mostly pointless endeavour

to be honest, i've come to the conclusion that an absolute formula for primes would be so inelegant (like fermat's last theorem) that i wouldn't like the solution anyway. so i'm just going to assume that there is a proof, but it's unprovable. kinda like proving whether the euler-mascheroni constant is irrational, or the fucking collatz conjecture.