Hidden Secrets of all existence in Prime Numbers?

First, it is all just data that shows the variety of those that already looked into these predominant numbers, there are some amazing figure heads here. I was shocked to find so much information available on these simple numbers, and that I was way too late to add anything to this knowledge, so I shared what I discovered as I learned about them myself.

Second I would have to reverse the question. What did you learn from them?

It’s little tidbits of knowledge that sometimes show us the utmost in this reality. Haiku …
 
Springing from the discussion on Ark's blog, here's some fun with prime numbers.

For starters, using Wolfram's Mathematica's function Prime[n], which returns n-th member of the infinite set of prime numbers, a 10×10 table of prime numbers looks like this:

PrimeTable10 = Partition[Table[Prime[n], {n, 100}], 10] // TableForm ;
{ {2, 3, 5, 7, 11, 13, 17, 19, 23, 29},
{31, 37, 41, 43, 47, 53, 59, 61, 67, 71},
{73, 79, 83, 89, 97, 101, 103, 107, 109, 113},
{127, 131, 137, 139, 149, 151, 157, 163, 167, 173},
{179, 181, 191, 193, 197, 199, 211, 223, 227, 229},
{233, 239, 241, 251, 257, 263, 269, 271, 277, 281},
{283, 293, 307, 311, 313, 317, 331, 337, 347, 349},
{353, 359, 367, 373, 379, 383, 389, 397, 401, 409},
{419, 421, 431, 433, 439, 443, 449, 457, 461, 463},
{467, 479, 487, 491, 499, 503, 509, 521, 523, 541}}.

It looks easier to read if transported from Mathematica as a PNG file, instead of just copy-pasting:

PrimeTable10.png.

Things started to look interesting when additional properties of being a prime number were taken into account, which ultimately produced the PrimeGrid (explained below). Using Mathematica, one possibility of creating this grid of prime numbers, the dwellings of the mystics, would be:

Priming[n_, k_] := NestList[ Prime, Prime[n], k - 1];
PrimeGrid[n_] := Partition[ Flatten[ Table[ Priming[i, j], {i, n}, {j, {n}} ]], n].

Here's how PrimeGrid(7) looks like in Mathematica:
PrimeGrid7.png.

It looks easier to read when inverted upside down, so that prime numbers lower in order are below those of higher order, in addition to adding natural numbers as their origins below the first row of such a table. Unfortunately, the Table option on the Forum appears to be too consuming to do that here and now, so without further ado below is PrimeGrid(12) as obtained by Mathematica, i.e. 12×12 array or grid of prime numbers with additional qualities of being a prime number.

PrimeGrid12.png

Tridimensionality can be visualized for starters, with the plane of natural numbers below and additional planes of the above grid, starting with the row corresponding to how high you go, above the plane/grid shown here above.

In short, first row from above are the prime numbers, going as far as you like and know them. Next row is obtained by applying the number values, those of being a prime number, to the residing row. In practice, 1st prime number is 2 and on the second place in 1st row is 3, 2nd prime number in order, and so 3 becomes first member of 2nd row. It continues like this all the way from the first column on the left. For the next row, you apply the same procedure. First prime number is 2, on the 2nd place in 2nd row is 5, being 3rd prime in order as 3 stands on the 2nd place in the prime number set.
 
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Springing from the discussion on Ark's blog, here's some fun with prime numbers.

For starters, using Wolfram's Mathematica's function Prime[n], which returns n-th member of the infinite set of prime numbers, a 10×10 table of prime numbers looks like this:

PrimeTable10 = Partition[Table[Prime[n], {n, 100}], 10] // TableForm ;
{ {2, 3, 5, 7, 11, 13, 17, 19, 23, 29},
{31, 37, 41, 43, 47, 53, 59, 61, 67, 71},
{73, 79, 83, 89, 97, 101, 103, 107, 109, 113},
{127, 131, 137, 139, 149, 151, 157, 163, 167, 173},
{179, 181, 191, 193, 197, 199, 211, 223, 227, 229},
{233, 239, 241, 251, 257, 263, 269, 271, 277, 281},
{283, 293, 307, 311, 313, 317, 331, 337, 347, 349},
{353, 359, 367, 373, 379, 383, 389, 397, 401, 409},
{419, 421, 431, 433, 439, 443, 449, 457, 461, 463},
{467, 479, 487, 491, 499, 503, 509, 521, 523, 541}}.

It looks easier to read if transported from Mathematica as a PNG file, instead of just copy-pasting:

View attachment 100413.

Things started to look interesting when additional properties of being a prime number were taken into account, which ultimately produced the PrimeGrid (explained below). Using Mathematica, one possibility of creating this grid of prime numbers, the dwellings of the mystics, would be:

Priming[n_, k_] := NestList[ Prime, Prime[n], k - 1];
PrimeGrid[n_] := Partition[ Flatten[ Table[ Priming[i, j], {i, n}, {j, {n}} ]], n].

Here's how PrimeGrid(7) looks like in Mathematica:
View attachment 100414.

It looks easier to read when inverted upside down, so that prime numbers lower in order are below those of higher order, in addition to adding natural numbers as their origins below the first row of such a table. Unfortunately, the Table option on the Forum appears to be too consuming to do that here and now, so without further ado below is PrimeGrid(12) as obtained by Mathematica, i.e. 12×12 array or grid of prime numbers with additional qualities of being a prime number.

View attachment 100415

Tridimensionality can be visualized for starters, with the plane of natural numbers below and additional planes of the above grid, starting with the row corresponding to how high you go, above the plane/grid shown here above.

In short, first row from above are the prime numbers, going as far as you like and know them. Next row is obtained by applying the number values, those of being a prime number, to the residing row. In practice, 1st prime number is 2 and on the second place in 1st row is 3, 2nd prime number in order, and so 3 becomes first member of 2nd row. It continues like this all the way from the first column on the left. For the next row, you apply the same procedure. First prime number is 2, on the 2nd place in 2nd row is 5, being 3rd prime in order as 3 stands on the 2nd place in the prime number set.

Fourth row springs from the 3rd just alike those before it; you take the set in the 3rd line of the table, see who's on the 2nd place in order who so becomes 1st in order in the new line, and continue. To elaborate, for example 8th row of the table are de facto the prime numbers being exactly 8 times prime numbers, meaning you applied the procedure described above, exactly 7 times to origin 1st row.

If you wish to find the members of your columns, you may now follow the ordering among the original set of the prime numbers.
For example, 4th column members stem from number 7, 4th prime number in order which so becomes the foundation of this pillar. Step next to number 7 is reserved for 7th prime number in order, that of 17, which gives number 59, as 17th prime number in order, on the 3rd step. On the 4th step, being a central piece of the 7×7 table in quote, sits 277, being 59th prime number in order. In such a manner opening quadrant of your table is filled.

Some associations to for example musical octaves and the Rays of Creation or Law of Seven seem to lurk around those dwellings of the mystics above, and hopefully these 'reviving' posts may spark a fruitful discussion in the spirit of the title of this Forum thread.

Cheers!
 
Here's an example of tables described above presenting different possible perception points. Unfortunately, phone cam decided to play uncooperatively and blurred certain parts, but hope you'll get an idea of how they might look like.

IMG_20240819_070309.jpg
IMG_20240819_070254.jpg
 
Attached is a possible representation of a 'job well done' in a sense of a voyage to the stars and galaxies all the way to our Divine Mother's bossom and right back into the human heart.

Let the Faith of Caesar live within us, if you choose so, as this is Free Will universe after all.

IMG_20240820_152026.jpg


IMG_20240820_152104.jpg
 
All 4 planar perspective possibilities combined, yield a nice representation of Ark's statements from his "Prime numbers are the dwellings of the mystics" blog post, namely the first one in quote box below:
My Belief
I prefer to start from symmetry and let it break. You can call me an "aperionist".

Symmetry Over Chaos
Starting from chaos doesn't attract me. I often leave the question of order's origin unanswered.

Beauty and Love
At most, I suggest that order arose from beauty or love.

Prime Numbers
Pressed for an answer, I propose that in the beginning, there were prime numbers. What could be more fundamental than prime numbers?

The First Principle
In essence, prime numbers embody the essence of the beginning for me. Their purity and simplicity are unmatched.

For the purpose of brevity and clarity, let's use only the first quintet of prime numbers as the base for this representation, {2, 3, 5, 7, 11}. The innermost 5×5 square of such a "table", which turned out to appear like a diamond due to my poor skills at centering and resizing the table cells here, if that's even possible without spending whole night for the sake of an appearance, then looks like this:

31
311131
311151131
17115351117
11753235711
17115351117
311151131
311131
31

Evidently, we have a highly symmetric situation, with no specific designation or differentiation between left/right or front/back, nor between up/down. If we flip this "table" around horizontal or vertical axis, we end up with the same one as the one we started with.
Only difference that can be perceived is that between vertical and horizontal, and even that is not set in stone as both main diagonals are identical, {31 - 5 - 2 - 5 - 31} in this representation, and flipping the "table" around both changes vertical to horizontal and vice versa.

Well, there could of course be other things symmetric about the "diamond table" above not mentioned in this short expose, and I hope that a keen observant eye will be paired with a freely dancing fingers so to complement what's been written above.

We could say that this representation presents a "pure unbroken primordial symmetry" or a "perfect state" of things.
A sort of a downside to this, from the learning point of view, is that this perfectly symmetric state is exactly that, a "perfect" state, sort of a "static" state where nothing changes as there's no need to change anything because it's perfect, perfectly and beautifully symmetric state.

So, for learning purposes, let's break this symmetry by introducing the illusion of separation which will naturally also bring the duality.
What that means in practice is that we won't align all 4 possible planar "perspectives" from previous posts in the thread in the overlapping manner like we did in the case of the "perfect symmetric table" above, but we'll keep their "identities" sort of intact, and align them in diagonal pairs around the newly introduced central table cell, sort of a "hearts" of these now freshly baked "imperfect tables".

There are two main possibilities for the alignment: we can align our diagonal pairs, meaning upper right with lower left and upper left with lower right or in standard mathematical nomenclature 1st quadrant with the 3rd and 2nd quadrant with the 4th, either vertically or horizontally, respectively, meaning one pair for example vertically, while the other pair will be aligned horizontally in that representation.

The difference between the two alignment possibilities displayed below comes into play when cycling is introduced, meaning moving from one quadrant to another which could be done in clockwise and counter-clockwise fashion, as that will then give birth to two types of sort of learning spirals, outward going and inward going one, depending if the transition between the quadrants is done towards higher numerical values or lower ones, respectively.

Let's first align upper right with lower left horizontally, which means that at the same time upper left and lower right are aligned vertically.
The resulting "imperfect table" looks like this:

31
311131
311151131
17115351131
117532351117
117532💖235711
171153235711
31115351117
311151131
311131
31

Let's just say that cycling clockwise in this alignment representation above results in an outward going spiral, while the same cycling direction in the representation where upper right and lower left are aligned vertically, as shown below, makes an inward going spiral.

31
311131
311151131
31115351117
171153235711
117532💗235711
117532351117
17115351131
311151131
311131
31

Although our initial symmetry is broken within these "imperfect tables", meaning we now can differentiate left from right or front from back, and up from down, certain "residual" symmetries have nevertheless been preserved or inherited by both of these representations.
One of those "inheritances" would be the famous "As above, so below" saying, that Ark used to close his "Monkeys, UFOs, and Quantum Fractals: A Mind-Bending Journey through Relativity and Imagination" blog post with, which simply means that the triangle at the bottom reflects the triangle at the top of our "imperfect tables".

As my behind got rather sweaty while composing all these "diamond-like tables", a sort of a post wrap-up might be convenient at this point, by extending the invitation to all interested in spotting other "inherited" inner symmetries therein, and also "symmetry breaking" elements in them that give rise to knowing left from right or front from back and where usually head resides compared to the feet as well.
 
This is another fascinating information, so, I like to know if other have more thoughts about this subject.
The C's are talking about a Trinity spiritual based math system. Not base 10 as we normally use, but closer to a base 3 system but not exactly.

The C's said "WHO are YOUR prime numbers". Everyone is a Trinity composed of 3 lower centers, thought, body, and emotion, or in other words the number 3. We also hope to develop a soul which is also a Trinity, and composed of our 3 higher centers, thought, body, and emotion. All together we have 6 centers, 3 lower and 3 higher. You could also think of this as a 2Trinity, the number 33, or as I like to call it a Tritwoity. (This is why you have 33rd degree Freemasons for example.)

A: Yes, thank you Arkadiusz!!!!
..all of creation, of existence, is contained in 1, 2, 3!!! Look for this when you are trying to find the keys to the hidden secrets of all existence... They dwell within. 11, 22, 33, 1/2, 1/3, 1, 2, 3, 121, 11, 111, 222, 333, and so on! Get it?!?!

The C's say "They Dwell within".

The number 11 would mean one lower center along with its corresponding higher center, for example your lower physical body along with your soul body.
The number 22 would mean two lower centers along with 2 corresponding higher centers, for example your lower thought center, higher thought center, and lower emotional center, higher emotional center.

Fractions would apply to either out of 6 total centers or 3 centers.

The 111, 222, and 333 would apply to an individual who has merged their higher and lower centers, like the Toltec's call the third attention.


Graphical Representation.

2trinitylife.png

More here: 2Trinity | Northern Orthodox Church
 
For those following the tables of prime numbers Odyssey so far, a little treat at this point of the journey (thanks to Ark for a hint and inspiration with images in today's blog post :flowers:).

In the session 08/08/1998, the C's mentioned three-dimensional matrix 12×12×12:
Q: ... (A) In this session with Santilli there was repeated at least twice the term 'matrix.' Laura made a comment that maybe it was a three dimensional matrix. So I was thinking about this matrix and I have two possibilities. If it is related to the number 3, it can be a matrix that is flat and 3 by 3. Or, it can be any matrix that is three dimensional rather than flat. Which of these, if any, is the concept mentioned in the session?

A: Three dimensional 12 by 12.

Q: (A) 12 by 12 by 12?

A: Yes.

Q: (A) Why number 12? What is so particular about number 12?

A: Try it and see.

There's an interesting and "funny" possibility to get such a matrix using the previously described tables of prime numbers.
Instead of the first quintet of primes which was used for the table base in previous post, use first 11 prime numbers. Make the second representation for example, that is the "imperfect table" where upper right and lower left were aligned vertically. The result is a 12×12 square. Repeat the procedure for the other representation, that is now align upper left with lower right vertically, and get another 12×12 square. Intertwine and align the two tables and voila, there is the 12×12×12 3d matrix of the prime numbers the C's were referring to.

Attached is the result when using just half of the second 12×12 table so only folding it was needed to get the 3d perspective. It's also not completely filled all the way to the number 9 737 333 which is the first prime of 11th order, dots stand in place of missing numbers.

IMG_20240912_012315.jpg
 
Since the image in previous post might have given the misleading idea about how to reach the third spatial dimension of the 12×12×12 matrix of prime numbers discussed there (which is basically just a bit 'hairy' cube composed of 12×12×12 little cubes or building blocks or stones), that is its height or depth, I resolved to some elementary drawing to hopefully eliminate eventual ambiguities.
And since according to UTC we are already in Friday the 13th, date and day with a bad aura due to also Templars allegedly meeting their sorrow end in 1307 AD, maybe it's just the right time to deal with some old injustices as well.

While aligning possible perspective viewpoints of the "prime cube or matrix", I followed natural human body 'arrangement', that is if viewed from the front side for example, left and right are reversed, and if viewed from above, back points up while front points down.

Three main planar viewpoints or perspectives, giving birth to sort of a skeleton of the "prime cube", are then:

a) basal plane viewed from above, spanned by first eleven prime numbers that make the base of the 12×12×12 "prime matrix" as denoted in previous post, doing sort of rings or rounds around the central 'heart' cube or stone. The outermost ring is made of 4×11 stones marking 11th prime number, number 31, while the innermost ring is composed of four 2s (1st prime number). Each successive ring until number 31 is reached gets 4 additional stones compared to its immediate predecessor, that is 2nd prime number for example, number 3, makes the ring of 4×2 stones, while 3rd prime ring (number 5) has 12 stones, 4th ring (number 7) 4×4 building blocks, and so on.

IMG_20240912_205659.jpg


b) side view looking from the right hand side where front appears on the right and back on the left side. Image is unfortunately rotated clockwise for 90°, but orientation of the numbers points where is up (right side of the rotated image). Upper right is aligned horizontally with lower left and height or depth are obtained by going higher in order of primeness until 11th order is reached, that is the prime number 9 737 333 sits on top and on bottom of the "prime cube or matrix".

IMG_20240912_205812.jpg


c) frontal view where left and right are reversed (like looking at human body from the front side). Upper right and lower left are aligned vertically, but image is again rotated by 90° clockwise (see word "up" on the right side of the rotated image for example to get proper perspective). Height and depth are obtained as in previous image b).

IMG_20240912_210124.jpg


When all three perspectives or viewpoints are spatially properly combined, they result in 3d representation of the "prime cube" as shown in the next image, that is the upper part of frontal view looked at from the right hand side.

IMG_20240913_013424.jpg


As said before in the post, this is just sort of a skeleton for the "prime cube", composed of three main planes or spatial diagonals. The rest of the "prime cube's" body is made of other stones or building blocks or smaller cubes as described in previous posts in the thread.
When completely fulfilled "prime cube" is looked upon from any side, only outermost or corner stones are visible. Final image here shows exactly those "prime cube" corner stones when observed from above, that is its frontal part (front is on the left side of this 90° counter-clockwise rotated image) as back part looks identical due to symmetry, as does the sight from bellow as in the "As above, so below" fashion.

As expected, the outer ring of corner stones is made of those 44 stones with number 31 written on them, as that number is 11th prime number, while the innermost part, of heart of the corner stones, is marked by 25 blocks of number 9 737 333, prime number of 11th order that is also on the bottom and on the top of main "prime cube or matrix" axis.

IMG_20240913_013610.jpg

Edit: removed some left over text and image that didn't belong to completed post body.
 
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In this week's posts here, I made several sort of erroneous statements and going over them, apart from setting myself straight, provides me also with an opportunity to shed some additional light on the prime cube presented in previous post.

So, for learning purposes, let's break this symmetry by introducing the illusion of separation which will naturally also bring the duality.
Sort of an error in this statement is that duality was already implicitly present even within that "perfect state" by evident difference between vertical and horizontal arrangements of prime numbers in the table. Going with what the C's said about the introduction of duality into the learning cycles, it then appears that that perfect table and following imperfect ones, including the resulting prime cube, represent sort of a knowledge of short wave cycles. As such, it is neither good nor bad, it just is, and it's our choices and actions, our alignment, and the situations, that determine which is which. By choosing the alignment, that is our affinity to gravitate either towards spirituality or physicality, we choose in a sense which side of the vertical becomes our "up" and which side becomes our "down".

My choice of alignment in that respect, which is reflected by the arrangements of imperfect tables in composition of the prime cube in previous post, although stated in a bit of a messy and ambiguous wording because of interchangeable sides like left <-> right on the images there due to different perspective viewpoints, as I realized today and will explicitly elaborate further on in this post, can be expressed by the signature which is part of the spiritual reading Artemis did for me, and can also be summarized by four words from the first verse of a prayer or a reading I recite on more than a daily basis usually both out-loud and silently in my mind: Free Will for All.

Another erroneous statement lies at the end of the previous post, in addition to probably giving wrong impression about the alignment I used when composing actual prime cube, although that can be correctly deduced from the 3d image representation of its skeleton.
I wrote that front part and back part of the corner stones when viewed from above are identical due to symmetry, which was also shown in the last image attached to the post, and that the same was valid when looked from below. Well, the key word there was the "symmetry", which was effectively broken by the alignment, as described in this post, so that top view corner stones image and accompanying text were not the correct representations of the actual prime cube's corner stones. The difference between the symmetric "perfect" and real "imperfect" prime cube, although seemingly small, is as large as difference between heaven and earth in terms of personal alignment and associated development, but when it comes to their corner stones consists only of different number of just two types of them.

Technically speaking regarding the corner stones, those sides that are aligned vertically, get an additional corner stone of 31 at the expense of one corner stone of 9737333 on the main branch pointing in the direction of that side, while other stones on that branch get shifted towards the central 9737333 corner stone for one position. All other corner stones remain on their places as shown in that last image in previous post. Visually, the difference between those two main branches of corner stones looks like this:

horizontal alignment311094312221152998780364839122697339737333973733397373339737333
additional 31 in vertical alignment9737333 removed in vertical alignmentcentral
corner
stone
vertical alignment3131109431222115299878036483912269733973733397373339737333

Since choice to align one part, upper or lower, of a side in one direction automatically leads to other part of that side being aligned in the other direction, there are always two sides that are aligned horizontally and two that are aligned vertically when viewed either from above or from below, with opposite parts of the sides belonging to one or the other. In practice it means that when I aligned upper-right with lower-left horizontally, lower-right was automatically aligned vertically with upper-left. And to compose the prime cube correctly, it also automatically led to upper-back being aligned vertically with lower-front and consequently lower-back to upper-front horizontally.

The choice of alignment is propagated throughout almost the whole of the prime cube in the sense of the arrangement and of the types of the prime numbers on the main branches therein, starting immediately from the first plane both above and below the basal one, similarly to what happens with our natural alignment and choices we make as we go on with our ordinary daily lives.

Apart from the basal plane which is "perfectly" symmetric on the exchange between left and right, and between front and back, there are also three planes at the top and on the bottom of the prime cube with that same characteristic. Sort of a last plane that still carries the information about the alignment is thus the 8th plane above or below the basal one. In my chosen alignment, the 8th plane above the basal one when viewed from above looks like this:

front
9737333
97373336483919737333
9737333648391527116483919737333
left2269733648391527115381527116483919737333right
9737333648391527116483919737333
97373336483919737333
2269733
back

Although there are probably infinitely many ways to "use" prime numbers and prime cube as our minds are limitless in their creative capacity, in a real practical down to earth sense they can be rather efficiently used in solidifying intention and will, setting the head and the heart in resonance and the being in a colinear direction with our goals and aims whatever we choose them to be.

Free will for all.
 
Another possible, practical and very useful "usage" of the prime numbers in the context of this revival and on a sort of a cosmic scale, equivalent to the 'job well done' post posted here in this thread cca 40 days ago, would be in completing/starting the Rays of Creation or closing/opening the octaves as they're presented by the Law of Seven.

The schematic diagram of such potential application might be represented by the following table.
IX​
VIII​
VII​
VI​
V​
IV​
III​
II​
I​
52711
5381
709
127
31
11
5
3
2
(1)​
52711
5381
709
127
31
11
5
3
(2)​
52711
5381
709
127
31
11
5
(3)​
15299
1787
277
59
17
7
(4)​
⬆​
52711
5381
709
127
31
11
(5)​
8527
1063
179
41
13
(6)​
⬆​
152991787
277
59
17
(7)​
2221331
67
19
(8)​
300143183
23
(9)​
439759910929
(10)​
⬆​
538170912731
(11)​
91915737
(12)​
⬆​
106317941
(13)​
19143
(14)​
21147
(15)​
24153
(16)​
⬆​
27759
(17)​
61
(18)​
⬆​
67
(19)​

Sort of predisposition to application depicted in the diagram would be the acquisition of knowledge and the development of being corresponding to present/current inhabited octave. Having met that precondition, starting from the stepping stone next to the last stone of the fulfilled octave, the developed being gets propagated guided by the acquired knowledge all the way to the completion of the next octave, marking the initial note or vibration or frequency for the next cycle.
 
Sort of predisposition to application depicted in the diagram would be the acquisition of knowledge and the development of being corresponding to present/current inhabited octave. Having met that precondition, starting from the stepping stone next to the last stone of the fulfilled octave, the developed being gets propagated guided by the acquired knowledge all the way to the completion of the next octave, marking the initial note or vibration or frequency for the next cycle.
Instead of apparently convoluted closing passage of the previous post quoted in the box above, that likely came across as a wise-acring as well, it would have probably been better in a sense of clarity and understanding, to have pointed out the underlying principle of the schematic table diagram depicted in that post: "Putting someone on the step behind you".
Even though that principle very likely became rather evident to the keen observant eye when looking at the table diagram in question.

Well, a Balkan old saying comes to mind, "Čovjek uči dok je živ", which would translate to English as "A man learns while he lives", and which turned out to resemble quite closely to the last passage from Seneca's "Liber X, ad Pavlinvm: de brevitate vitae", Ch 7, section 3:
"Vivere tota vita discendum est et, quod magis fortasse miraberis, tota vita discendum est mori."
for which Bing's AI Copilot wrote that the phrase translates to:
We must learn throughout our whole life, and, what might surprise you more, we must learn to die throughout our whole life.”
 
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