Friday, January 02, 2015

I believe there is a special property of primes which links them intrinsically with the movement of the torus, but 'proving' that is proving tricky, like trying to catch a rare butterfly, perhaps. I also believe that Midy's Theorem was an early glance into this property.

I've included a scanned page from my notes that is trying to look deeper into this movement. About halfway down is a graph which attempts to chart the toroidal movement in 1/7th (each dot represents one number between 0 and 9 ... it is easy to see that 0, 3, 6 and 9 do not appear, yet reveal themselves in the overall structure), and beneath that, 1/13th (although each number is represented, 0-9, the numbers 3 and 6 have double the activity, or double the neighbors in the repeating decimal, than each other number). This is what led to the image of the torus at the top, which shows 9 as the vector and 3 and 6 as the points around which the rest of the torus is spinning.


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Nice one Leben. :)
Thanks, Barbitone :)

Here's a scan which shows another way of looking at it, I think you'll like this as well ...
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I think your 1/7th idea has credence, if for instance you consider the 7 color map of the torus as explained by Stan Tenen and others...and the primes, when I studied them I was using the VBM torus skins and I found that a slightly new definition of primes was needed which is that no number that reduces to a 3,6 or 9 appear and all are odd numbers so 5,7,11,13,17,19 etc.... If you start with the regular vbm torus skin (1-8) and make larger tiles over the top of the skin (a large skin is needed) in resolutions of primes squared, I get a fractal repetition of the whole skin only on a larger scale and in the next axis rotation.Any tiling done that is 3,6 or 9 reduced, will be all mirror pairs; no dual doubling circuit and one spacing emenation line.
Like the true primes, the division by 7 gives only  repeating digits of 1,2,4,8,7 and 5. No 3,6,9. Whenever your t alking about the 1,2,4,8,7,5 your talking about the material w orld that is subject to duality and linear space/time etc... The spiral movement. The 3 and 6 are the oscillators - the spacers, and the 9 is the centre.So the torus uses squared primes to both create fractal resolutions and axis roations - axis roations in the sense that the rodin skin can have multiples of mirror pairs on different axis, and since the spiral movement moves on all 3 axis simultaneously (forward, down and to the side...) all combinations trinary oscillate and mirror.


Hey Leben, great work!

This method forms one of the basic concepts in developing number visualization systems. I will go into detail later, but here is a sculpture I created from the 1/7 pattern: Fluctua 142857 sculpture

Leben said:
Thanks, Barbitone :)

Here's a scan which shows another way of looking at it, I think you'll like this as well ...
Mane! That's an incredible piece of art, thank you for sharing. Is most of your work accessible from that website? I look forward to hearing more details later. Looking at your sculpture, I was immediately reminded of harmonic waveforms:



Barbitone~ I'm having a difficult time visualizing, do you have a way of showing what you are speaking about? When I have some more time (probably in a couple days), I will sit down and try to work it through :)

Whenever your t alking about the 1,2,4,8,7,5 your talking about the material w orld that is subject to duality and linear space/time etc... The spiral movement.

So true ...
Barbitone said: "I think your 1/7th idea has credence, if for instance you consider the 7 color map of the torus as explained by Stan Tenen and others ..."

I've looked into the 7-color map of the torus from the work of Arthur Young, and found it very interesting. I have yet to read his book "Reflexive Universe," however, but I have requested to borrow it from a friend. It's very interesting, the phi spiral that is created as a result of the toroidal color mapping:

I recently was playing around with graphing the changes between notes of the octave and saw something very similar, which I have not seen anywhere else (if anyone has further information which corresponds or sheds light on the following, please direct me). I divided a circle into 24 portions (the common factor of thirds, fourths and eights) so I could easily plot the change between notes. The first note, Re, takes 3 segments of the circle, or 1/8th. The second note, Mi, takes 6 segments total (3 additional segments from Re), or 1/4th of the total circle. Fa, 8 segments total (2 more than Mi), 1/3 of the circle, and so on, for each note. Graphing it linearly did not reveal much to me, but after plotting it in the circle, the spiral quickly showed itself:

This is the first true prime squared and reiterated over the original torus skin. The original torus skin, as you can see, has 1/8 multiplication on the vertical axis and the 4/5 multiplication on the horizontal axis. After expanding into the next fractal level, the axis are now 4/5 vertical, 2/7 horizontal.....
Okay ... I think I'm beginning to see what you're saying. So if the big tile was made by 7x7 squares all centered  ...  8/1 would become 4/5, 6/3 would become 3/6, 7/2 would become 8/1 and 4/5 would become 2/7.

Also, it seems that it's not really a new definition of primes, just another perspective on them ... they already happen to not reduce to 3, 6, or 9 and be odd. Right?
Yes. Each iteration is also a new axis - trinary rotation. There are only 3 different "true" torus skins but there are also the mirror inversions, so there are 6 but it is a symetrical set. 3 and 6 is the oscillation/polarizer and the 9/0 is the black/white hole(/whole). :)
Original primes include 2 and 3, and skip a bunch of numbers - In VBM terms, 5 is the first prime (in my opinion based on the torus skin) and most of the numbers that are missed in the original primes happen to be the squared primes - so starting with 5..........5x5=25, 7x7=49, 11x11=121, 13x13=169, 17x17=289.........
And you get a new circuit sequence ; 1-5-7-2-4-8

Leben said:
Okay ... I think I'm beginning to see what you're saying. So if the big tile was made by 7x7 squares all centered  ...  8/1 would become 4/5, 6/3 would become 3/6, 7/2 would become 8/1 and 4/5 would become 2/7.

Also, it seems that it's not really a new definition of primes, just another perspective on them ... they already happen to not reduce to 3, 6, or 9 and be odd. Right?
Beautiful ... the final geometries there are truly wonderful.

I see that all primes reduce to a number in the set 1, 2, 4, 8, 7, 5, and that the sequence for the first six primes certainly follows the pattern 5, 7, 2, 4, 8, 1 ... but the pattern seems to skip all over the place after that:

5, 7, 2, 4, 8, 1 ... 5, 2, 4, 1, 5, 7, 2, 8, 5, 7, 4, 8, 1, 7, 2, 8, 7 ...

It seems that the triple-triad symbol is a good representation of the path of the first six primes, but unless I'm failing to see a larger pattern, isn't quite a "circuit." Is that right? I will definitely be working with this :)

I came across the additional torus skins quite accidentally, myself ... I was playing with hexagonal tiling and saw that 9 only had six neighbors, 4 and 5 were 'offset,' yet it seemed appropriate that all the numbers should be touching 9. I supposed that if I couldn't see them, they must be 'above' and 'below' the paper. After playing around with that, the 3 "true" and the 3 "mirror" skins revealed themselves pretty quickly. One of things that caught my eye about the "mirror" skins was that 2x2 squares add to rows of 3, 6 and 9, versus the "true" skins where every 2x2 square equals 9, always.
"
I see that all primes reduce to a number in the set 1, 2, 4, 8, 7, 5, and that the sequence for the first six primes certainly follows the pattern 5, 7, 2, 4, 8, 1 ... but the pattern seems to skip all over the place after that:

5, 7, 2, 4, 8, 1 ... 5, 2, 4, 1, 5, 7, 2, 8, 5, 7, 4, 8, 1, 7, 2, 8, 7 ..."

No it works, look at it again and remember that you have to include all odd numbers that do not make 3,6 or 9.
I believe there is a special property of primes which links them intrinsically with the movement of the torus, but 'proving' that is proving tricky, like trying to catch a rare butterfly, perhaps. I also believe that Midy's Theorem was an early glance into this property.

I've included a scanned page from my notes that is trying to look deeper into this movement. About halfway down is a graph which attempts to chart the toroidal movement in 1/7th (each dot represents one number between 0 and 9 ... it is easy to see that 0, 3, 6 and 9 do not appear, yet reveal themselves in the overall structure), and beneath that, 1/13th (although each number is represented, 0-9, the numbers 3 and 6 have double the activity, or double the neighbors in the repeating decimal, than each other number). This is what led to the image of the torus at the top, which shows 9 as the vector and 3 and 6 as the points around which the rest of the torus is spinning.


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So this makes primes out of numbers like 25, 35, 55 and 65? That IS a slightly different definition ... lol

Does this circuit make any other appearances or have other properties?
Perhaps they aren't really primes so much but are connected somehow....I don't know, I just know what works in terms of patterns..... I think there was something else to this sequence and connected things but I cant remember without going through all my old notes, have a play and see....

Leben said:
So this makes primes out of numbers like 25, 35, 55 and 65? That IS a slightly different definition ... lol

Does this circuit make any other appearances or have other properties?

Hmm ... I think this symbol is incredibly significant, and have only encountered it before in the work of Keith Buzzell. Perhaps, the numbers signified by this circuit are similar to primes, yet have a unique function unto only themselves, such as permutated rotations of the toroidal axes?
Hey Guys, I couldn't help but read some of these posts.  I've been going back over primes lately and found some great info that I've been investigating, I found a Rodin paper below at this link, sounds like the one he talked about in some of the videos for solving primes.
I agree with Barbitone, the PRIME KEY is 5-7-2-4-8-1 but the key is in the exclusions which we already identified as being MULTIPLES OF PRIMES, that my friends is the key, I am trying to find a good way to explain it, but I feel like the PRIMES as discussed earlier are the two columns of numbers, which is one type of prime number.  But then to get the conventional primes (minus 1, 2 and 3) you apply these exceptions.  Let me know if you guys get this, it has gotten quite complex for me, and I'm trying to find the simplest way to show it with doing more than a vague explanations.

Cheers,

Riseball.

http://markorodin.com/1.5/publications
http://markorodin.com/media/PHYLLOTAXIS_PRIME_NUMBER_SIEVE-2007.pdf (around p15-16 about primes)
A prime issue with prime numbers is that their concept lacks poetry. Imagine a fabric of numerical relationships, beginning with 2, which connects to four, 3 to 6, 12, 15, and 18, 4 to 8, 12, and 16, 5 to 10, 15, and 20, 10 to 20, 8 to 16 and 24, and so forth. Each prime number is a void in the fabric of numerical relationships, as no previous threads except 1 and itself achieve its value; hence, any combination of two voids will equal a void, or in other terms, a multiplication of any two primes will equal a sub-prime value. As you may imagine, the fabric of numerical relationship's complexity is reciprocal to the amount of integers; this is why we initially see the prime key, 157248, and then the pattern appears to skip; in order to perceive the prime pattern, a new class of numbers is defined; prime, sub-prime, and non-prime numbers. Beautifully, any possible multiplication of prime numbers is hierarchically included in the 572481 pattern; to further the point, we can break down subprime multiplications, such as 25x5, into 5x5x5, or 35x7 into 5x7x7.

Yonder thy poetry, a comprehensive definition is upon us; not simply definition, but a perspective which enables further integration of prime numbers into Vortex Math.

1 is the first prime number, naturally. 2 and 3 are not prime, as they are excluded from the prime number pattern, 157248. 5 is the second prime number, preceding 7, then 11, 13, and 17. 25 is prime, or technically sub-prime, because it can be written as the product of primes; 5x5. 35 is the next subprime integer, written as 5x7. 49 is the next subprime, 7x7. Then 55, 5x11; 65, 5x13; 77, 7x11; 85, 5x17. As you may see, the hierarchy occurs in an overlapping fashion;

5x5
5x7
5x11
7x7
5x13
7x11
5x17
7x13
5x19
5x23
7x17
5x5x5
7x19
11x13
5x29
5x31
7x23
13x13
5x5x7
5x37
11x17
7x29
5x41
11x19
5x43
7x31
13x17
5x47
5x7x7
11x23

and so forth 
1
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Mane, I couldn't agree more, I've come to the same conclusion that there are your groups of sub-primes which are highlighted below in red, which are derrived from the PRIME KEY.  One could argue though that 1 is not prime just for the simple fact that it's exceptions are all relevant as shown below, but only to the same numbers for which 1 is a multiple of with a sub-prime number.  Is is possible that 5 is the first prime?  It does have huge significance to PHI (1.618...)

All the numbers in red will be sub-prime exceptions to infinity, but in the row 1, only the numbers which match any of the sub-prime numbers will be sub-prime (1, this row to me exceplifies the PRIME numbers, whereas all the red are SUB-PRIME.

In my mind the best way I think of using the PRIME KEY (572481) is it is the base for all subprimes numbers, then using the same key one could also apply it to derrive all PRIME numbers from it.




The above forms some other KEY PATTERNS.

Hope this helps anyone with their search for primes, this has cleared up much for myself.

Cheers!

Riseball

Mane said:
A prime issue with prime numbers is that their concept lacks poetry. Imagine a fabric of numerical relationships, beginning with 2, which connects to four, 3 to 6, 12, 15, and 18, 4 to 8, 12, and 16, 5 to 10, 15, and 20, 10 to 20, 8 to 16 and 24, and so forth. Each prime number is a void in the fabric of numerical relationships, as no previous threads except 1 and itself achieve its value; hence, any combination of two voids will equal a void, or in other terms, a multiplication of any two primes will equal a sub-prime value. As you may imagine, the fabric of numerical relationship's complexity is reciprocal to the amount of integers; this is why we initially see the prime key, 157248, and then the pattern appears to skip; in order to perceive the prime pattern, a new class of numbers is defined; prime, sub-prime, and non-prime numbers. Beautifully, any possible multiplication of prime numbers is hierarchically included in the 572481 pattern; to further the point, we can break down subprime multiplications, such as 25x5, into 5x5x5, or 35x7 into 5x7x7.

Yonder thy poetry, a comprehensive definition is upon us; not simply definition, but a perspective which enables further integration of prime numbers into Vortex Math.

1 is the first prime number, naturally. 2 and 3 are not prime, as they are excluded from the prime number pattern, 157248. 5 is the second prime number, preceding 7, then 11, 13, and 17. 25 is prime, or technically sub-prime, because it can be written as the product of primes; 5x5. 35 is the next subprime integer, written as 5x7. 49 is the next subprime, 7x7. Then 55, 5x11; 65, 5x13; 77, 7x11; 85, 5x17. As you may see, the hierarchy occurs in an overlapping fashion;

5x5
5x7
5x11
7x7
5x13
7x11
5x17
7x13
5x19
5x23
7x17
5x5x5
7x19
11x13
5x29
5x31
7x23
13x13
5x5x7
5x37
11x17
7x29
5x41
11x19
5x43
7x31
13x17
5x47
5x7x7
11x23

and so forth
5 as the first prime is an interesting notion, but after certain insight, the pattern connects to Vortex Math as 157248;

We read 124875 linearly, as with 142857, because the sequences have linear symmetry, with 1 and 8, 2 and 7, 4 and 5; thus, polar pairs enable reading the prime key, 157248, which has an expanding, or contracting symmetry, as -->751 and 248, or <--157 and 842;




p.s. your images are not viewable.

Riseball said:
Mane, I couldn't agree more, I've come to the same conclusion that there are your groups of sub-primes which are highlighted below in red, which are derrived from the PRIME KEY.  One could argue though that 1 is not prime just for the simple fact that it's exceptions are all relevant as shown below, but only to the same numbers for which 1 is a multiple of with a sub-prime number.  Is is possible that 5 is the first prime?  It does have huge significance to PHI (1.618...)

All the numbers in red will be sub-prime exceptions to infinity, but in the row 1, only the numbers which match any of the sub-prime numbers will be sub-prime (1, this row to me exceplifies the PRIME numbers, whereas all the red are SUB-PRIME.

In my mind the best way I think of using the PRIME KEY (572481) is it is the base for all subprimes numbers, then using the same key one could also apply it to derrive all PRIME numbers from it.




The above forms some other KEY PATTERNS.

Hope this helps anyone with their search for primes, this has cleared up much for myself.

Cheers!

I've been working a bit with the vortex primes myself lately, so I'm really glad you posted here Mane ... it truly illustrates the power that many have when they work together. Has everyone had a happy new year?

Below, I have arranged a table that lists each number, 1 through 300, in 10 rows of 10 and reduced to their mod9 congruence. Red numbers are traditional primes, blue numbers are "sub-primes" or prime-composites or whatever we decide to call them (I feel it should be noted here that ANY number can be reduced to prime factors, so to say that it is unique that our sub-primes are the product of two or more primes is insufficiently unique, in my opinion). However, this table illustrates the presence of 3, 6 and 9 in the underlying geometry of vortex-prime distribution. As you can see, primes and sub-primes stack to add to either 3, 6 or 9 (in mod9), in continued alternation (3, 6, 9, 3, 6, 9 ...). There are other significances which I will leave for the viewer to discover :)

It's also interesting to see it in 6 columns instead 10. Below, the family number groupings align vertically (where above, they are shown in alternating diagonal scrolling which loops around as if on a cylinder), and the primes and sub-primes are in bold, the later also underlined.

1 2 3 4 5 6 (6)
7 8 9 1 2 3 (12)
4 5 6 7 8 9 (18)
1 2 3 4 5 6 (24)
7 8 9 1 2 3 (30)
4 5 6 7 8 9 (36)
1 2 3 4 5 6 (42)
7 8 9 1 2 3 (48)
4 5 6 7 8 9 (54)
1 2 3 4 5 6 (60)
7 8 9 1 2 3 (66)
4 5 6 7 8 9 (72)
1 2 3 4 5 6 (78)
7 8 9 1 2 3 (84)
4 5 6 7 8 9 (90)
1 2 3 4 5 6 (96)
7 8 9 1 2 3 (102)
4 5 6 7 8 9 (108)
Great work!

Interesting how the 5 column from the initial graph is a spine to the pattern.
I am intrigued by the residue pattern;

234 891 567

As for subprime factorization, the 157248 definition of primes states that 2 and 3 are not prime; therefore, prime factorization is unique to subprimes.


Leben said:
It's also interesting to see it in 6 columns instead 10. Below, the family number groupings align vertically (where above, they are shown in alternating diagonal scrolling which loops around as if on a cylinder), and the primes and sub-primes are in bold, the later also underlined.

1 2 3 4 5 6 (6)
7 8 9 1 2 3 (12)
4 5 6 7 8 9 (18)
1 2 3 4 5 6 (24)
7 8 9 1 2 3 (30)
4 5 6 7 8 9 (36)
1 2 3 4 5 6 (42)
7 8 9 1 2 3 (48)
4 5 6 7 8 9 (54)
1 2 3 4 5 6 (60)
7 8 9 1 2 3 (66)
4 5 6 7 8 9 (72)
1 2 3 4 5 6 (78)
7 8 9 1 2 3 (84)
4 5 6 7 8 9 (90)
1 2 3 4 5 6 (96)
7 8 9 1 2 3 (102)
4 5 6 7 8 9 (108)
Thanks, mane. By that definition of primes, it is certainly true!

The residue of which you speak, is also the doubling circuit (AND the nexus key) when graphed (i.e. 9 at the top of the circle and the other numbers wrapped down the sides, each inline with it's polar pair ... 3 and 6 switch sides, all the family number groups are still separated by 3, the new configuration still allows for both mod9 circuits to be traced) ... very, very interesting!

Here's some interesting geometry of prime numbers stuff I've enjoyed:

http://www.youtube.com/watch?v=sbjPwyPT1AI

http://www.youtube.com/watch?v=4_U8SygYleI
Hey Folks,
Leben I followed the youtube links and eventually ended up on this site  http://www.primesdemystified.com/ which I think you guys should find interesting. It involves something called the Croft Spiral Sieve. -Enjoy






Mane said:
5 as the first prime is an interesting notion, but after certain insight, the pattern connects to Vortex Math as 157248;

We read 124875 linearly, as with 142857, because the sequences have linear symmetry, with 1 and 8, 2 and 7, 4 and 5; thus, polar pairs enable reading the prime key, 157248, which has an expanding, or contracting symmetry, as -->751 and 248, or <--157 and 842;




p.s. your images are not viewable.

Thanks Mane, they should be viewable now.  I for one think that one needs to do the work to really understand all that is being shared here, and in doing so there are probably other interesting finds waiting to present itself.  The joy for me is in self-discovery!

Cheers!

Riseball

Riseball said:
Mane, I couldn't agree more, I've come to the same conclusion that there are your groups of sub-primes which are highlighted below in red, which are derrived from the PRIME KEY.  One could argue though that 1 is not prime just for the simple fact that it's exceptions are all relevant as shown below, but only to the same numbers for which 1 is a multiple of with a sub-prime number.  Is is possible that 5 is the first prime?  It does have huge significance to PHI (1.618...)

All the numbers in red will be sub-prime exceptions to infinity, but in the row 1, only the numbers which match any of the sub-prime numbers will be sub-prime (1, this row to me exceplifies the PRIME numbers, whereas all the red are SUB-PRIME.

In my mind the best way I think of using the PRIME KEY (572481) is it is the base for all subprimes numbers, then using the same key one could also apply it to derrive all PRIME numbers from it.




The above forms some other KEY PATTERNS.

Hope this helps anyone with their search for primes, this has cleared up much for myself.

Cheers!

Great work there, Riseball ... interesting to see how we were working in very similar directions, I only wish I had seen the images with your first post. It's peculiar how the 1-4-7 'prime exceptions' are always at a diagonal facing the origin, and the 2-5-8 exceptions are perpendicular.
Thanks Leben, I hope some of that helped, it sure helped me to see primes in a bit different way.
I would recommend also taking the patterns shown (prime exception key mod9) and mapping it on a 1-9 circle for the keys shown above.
572481 is on the 19 prime horizontal line, note (19 = 1)
427518 is on the 17 prime horizontal line, note (17 = 8)
These two are polar pairs acting in opposite directions of each other, as exceptions to find true primes.  This is also the pattern I believe Barbitone has shown previously.  But their are two other patterns.

781245  is the 5 prime horizontal line (5 = 5)
218754 is the 13 prime horizontal line (13 = 4)
These are polar pairs.

154872 is the 11 prime line (11 = 2)
845127 is the 7 prime line (7 = 7)
These are polar pairs.

If you map the numbers of these three(3) patterns, not in a circle but in a spiral you will these patterns spiral to infinity that will map every exception as well, I don't have pictures to post of this, but rather invite those interested to discover this for themselves if they wish.  I can post something if anyone is interested.

@ Leben, I watched the videos on utube, the one in particular with the triangles regarding the PRIMES, has anyone confirmed this?  I kind of follow where he was going with it, but it seemed as though the patterns changed line to line with how many triangles he used going down?  If anyone could explain this further I would appreciate it.  Personally if the math doesn't coincide the geometry then in my opinion it is incomplete or possibly wrong, so this could be a very strong arguement as to all the different prime numbers that are being discussed out there.

Cheers!

Riseball


Leben said:
Great work there, Riseball ... interesting to see how we were working in very similar directions, I only wish I had seen the images with your first post. It's peculiar how the 1-4-7 'prime exceptions' are always at a diagonal facing the origin, and the 2-5-8 exceptions are perpendicular.

mod81 polar pairs with prime distribution;


1 2 4 8 16 32 64 47 13 26 52 23 46 11 22 44 7 14 28 56 31 62 43 5 10 20 40
80 79 77 73 65 49 17 34 68 55 29 58 35 70 59 37 74 67 53 25 50 19 38 76 71 61 41

mod81 reciprocals with prime distribution;


1 2 4 8 16 32 64 47 13 26 52 23 46 11 22 44 7 14 28 56 31 62 43 5 10 20 40 80

41 61 71 76 38 19 50 25 53 67 74 37 59 70 35 58 29 55 68 34 17 49 65 73 77 79

there is an interesting symmetry between 2:5 and 7:4 prime/nonprime combinations

p.s.

has anybody tried constructing a higher modular torus skin? I am attempting a mod81 skin, and there is an issue with reciprocals; they line up in mod9, but mod81 is scrambled.

Since 'conhersu one-time' posted a link to http://www.primesdemystified.com the site added a page that should be of great interest to this group: It explores the newly discovered 'Magic Mirror Matrix,' a mathematical object that reveals the perfect symmetry in the factorization sequences ultimately determining the sequence of prime numbers. Not only that, but it contains a transfrom hidden in plain sight that reveals an embedded Vedic Square: http://www.primesdemystified.com/magicmatrix.html 

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