Beyond Decimal

Beyond Decimal

Beyond Bases 2-10

The Quintessential Number

More on 10

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As before:

2701 = 37×73 and 2701 + 1072 = 3773

This supreme symmetry is so rare that there is only one known instance in the entire decimal (base 10) number system!

How about in other number systems?

We commonly use the base-10 (decimal) number system where there are 10 possible digits 0-9. But there are other ways to represent numbers.

For example, in the Binary (base-2) number system, only two digits are used: 0 and 1
In the Base-3 system, only 3 digits are used: 0,1,2
In the Base-4 system, only 4 digits are used: 0,1,2,3

Here is a conversion table between them:

Conversion Table
Decimal (Base 10)	0	1	2	3	4	5	6	7	8	9	10	11
Binary (Base 2)	0	1	10	11	100	101	110	111	1000	1001	1010	1011
Base 3	0	1	2	10	11	12	20	21	22	100	101	102
Base 4	0	1	2	3	10	11	12	13	20	21	22	23

Let us see if there are other solutions of the supreme symmetry in other number systems.

A scan of 200 million integers for bases 2 through 10 reveals one single other solution!

In the base 7 number system:
52₇×25₇=2023₇ and 2023₇+3202₇=5225₇

Is this solution also related to Genesis 1:1?

Incredibly, if we convert these numbers back to decimal (base 10) to see what they are:

52₇ = 37
25₇ = 19
2023₇ = 703

This solution converts back to none other than:

703 = 19×37

The Gematria of the last two words in the verse (which contains 7 letters).

Interestingly, the letter expansion (Milui) of these two words gives 2701

Letter Expansion of ואת הארץ
ץ	ר	א	ה	ת	א	ו
צדי דלת יוד	ריש יוד שין	אלף למד פי	הי יוד	תאו אלף ואו	אלף למד פי	ואו אלף ואו
558	890	275	35	531	275	137
Total=2701

These two share other symmetries such as:

Small Gematria (Ketana) of 1st verse = 82
Ordinal Gematria of וְאֵ֥ת הָאָֽרֶץ = 82
Number of Words of 1st verse = 7
Number of Letters of וְאֵ֥ת הָאָֽרֶץ = 7

It seems this is because וְאֵ֥ת הָאָֽרֶץ corresponds to the Sefirah of Malchut which includes everything (Aderet Eliyahu).

What about beyond base 10? Mathematicians and programmers commonly use up to 36 bases corresponding to A-Z and 0-9.

A scan of 8 million primes in bases 11-36 reveals an extra 3 solutions!^[1] (more primes causes my PC to overflow and crash in the manipulations)

In base 22:
3JCFF₂₂ × FFCJ3₂₂ = 2H26969A21₂₂ and 2H26969A21₂₂ + 12A96962H2₂₂ = 3JCFFFFCJ3₂₂

In base 28:
9J₂₈ × J9₂₈ = 6J03₂₈ and 6J03₂₈ + 30J6₂₈ = 9JJ9₂₈

In base 31
4CTG₃₁ × GTC4₃₁ = 2CR2E202₃₁ and 2CR2E202₃₁ + 202E2RC2₃₁ = 4CTGGTC4₃₁

However, of these 3 solutions, only the base 28 one is a true solution.

For in 2701=37×73 there is an extra symmetry that 37 is the mid-point of 73.

Center Point

37 is the exact center point of 73

1--------------------73

^
37

If we include this criteria, then only the base 28 solution fits (just like in 703=19×37, 19 is the midpoint between 1 and 37).

We can see this more clearly if we convert it back to decimal.

What is the base 28 solution in decimal (base 10)?

9J₂₈ = 271

J9₂₈ = 541

6J03₂₈ = 146611

Thus, in decimal (base 10) this number is none other than:

146611 = 271×541

541 is the Gematria of Yisrael!

Gematria of Yisrael
ל	א	ר	ש	י
30	1	200	300	10
Total=541

And 271 is the midpoint between 1 and 541.

Center Point

271 is the exact center point of 541

1--------------------541

^
271

As before, the Milui of Yisrael = 2701 - and the first verse has 28 letters.

The milui (letter expansion) of Yisrael = 2701

Letter Expansion of Yisrael
ל	א	ר	ש	י
למד מם דלת	אלף למד פה	ריש יוד שין	שין יוד נון	יוד ואו דלת
588	270	890	486	467
Total=2701

Rashi's commentary on the Torah expounds the word "Beresheit" from the Midrash: "G-d created the world for the sake of the Torah, which is called (Prov. 8:22): 'the beginning of His way', and for the sake of Yisrael who are called (Jer. 2:3) 'the first of His produce'..."

As for 146611, perhaps this is a hint to 611 = Torah and 146 = 73×2 (Wisdom×Beit, both 73 and Beit refer to wisdom as before).

It all goes back to the Triangle of 28 Letters. As we saw last time, the central "Yud" is "wisdom" then the inner triangle is Torah (611) and the outer triangle is the "Peh" (mouth) which corresponds to the Sefirah of Malchut. As known, Yisrael likewise corresponds to "Malchut".

To summarize the criteria of these "divine numbers"

two DISTINCT prime factors which are mirror reflections - ex.37×73=2701. Thus, 2701 is a semi-prime number
(not 9×9=81 since factors are neither distinct nor prime. also mirror reflection is trivial).
prime factors revealed when added to its own mirror reflection - ex.2701+1072=3773
prime factors which are mid-points of each other, ex.271 is exact midpoint between 1 and 541.

Thus, in number bases 2-36, only 3 known solutions exist and they are all related to Genesis 1:1!

A scan beyond base 36 shows more solutions starting from base 70, some with very important numbers related to Genesis 1:1.^[2].

As to the significance of semi-prime numbers and midpoint symmetry, I asked Oren Evran, an Israeli expert in Genesis 1:1. He replied:

A semi prime number has a meaning of a very robust construction. They are in one sense as important as primes. For the semi primes are so robust that they are very strong building blocks, but at the same time they are made of other blocks. Therefore if those other blocks (primes) are center points of one another the semi prime "building" you are looking at has a special shape of Figurate Triangular number which is like 2701 and it has more meanings to it way beyond this as geometrically speaking center points factors that are primes would always be odd (not even) and therefore it will have a center point of it's own and the Triangular would have inner-inclusions just like 2701.

2701 is also unique in the center-point triangle = T37 as you know etc.

Anyway, I think that this should be the default for the simple reason stated above and to continue explaining why I can go on for a long time

So it seems there are other solutions besides 2701=37×73
Is there anything unique about 2701 then?

Yes! In the section "Divine Symmetries", we showed that the PRIME INDEXES of 37/73 also have the same mirror symmetry. Namely, 37 is the 12th prime and 73 is the 21st prime.

Notice the PRIME INDEXES 12/21 are also MIRROR REFLECTIVE - just like 37/73.
Interestingly, 12/21 are also the very first pairs of numbers with mirror symmetry.

If we add this criteria, then there is NO OTHER SOLUTION in all number bases besides 2701 in base 10.
(we will see much more on the prime indexes in the section "Central Prime")
(as we will see, 2701 is also the ONLY triangle number in all of math whose inner triangle (703) is equal to its sum of thousands, namely 2+701=703. this has special meaning and works out only in base-10)

Notice also that 2701 and its prime factors all have digit sum = 10. The Hebrew Gematria system is base 10. (it goes 1,2,3,4,5,6,8,9,10,20,30..100,200..)

As to why 10, we saw earlier, "Bereisheit" means "with wisdom", for the world was created with divine wisdom, namely the Sefirah of Chochmah (wisdom) which is the 10th Sefirah (including "daat"). It is the highest Sefirah that encapsulates all the 10 as a chain-reaction, therefore you start with "1" and immediately jump to 10

See the super-symmetry of the gematrias and center points leading to 10, i.e. 73,37,19,10 - 1, as we explained in chapter "wisdom=Yud".

We humans are not able to grasp something that has no shape or location etc, therefore the initial wisdom men can grasp is called a point. It is the basic structure of everything and it is a location in space, so both are being sophisticatedly created at the same time.

The letter that represents the point is called YUD which is 10 and ultimately it is 1 in small gematria. This is the POINT of creation from which the 10 statements come from in the form of the 10 sefirot (heard from Oren Evron).

בְּרֵאשִׁ֖ית בָּרָ֣א אֱלֹהִ֑ים אֵ֥ת הַשָּׁמַ֖יִם

וְאֵ֥ת הָאָֽרֶץ

Total=2701

As before G-d's Name begins with the 10th letter - Yud.

The Maharal writes (Derech Chaim, Avot 3:13) that 10 represents a collective (klal). Thus, G-d's Name starts with the tenth letter Yud since G-d is collective in that He includes everything.

Likewise, all numbers after 10 are just an extension of this original collective of 10 (ibid).

The Yud is also the smallest letter reflecting the sublime non-physical nature of G-d. Yud is also the prime Hebrew letter in that all other Hebrew letters can be made from the "Yud" (Maharal).

Last but not least, the letter "Yud" means "hand", and of course, we normally have ten fingers and ten toes

But does "Yud" mean 10 because we have 10 fingers and toes or do we have 10 fingers and toes because "Yud" means 10? You decide.

Yisrael = 541 = 100th prime = 10² - the perfection of 10!

>> Next: Math and Reality

Footnotes

[1] see https://math.stackexchange.com/questions/3567551/ return to text
[2] A scan beyond base 36 shows the next solution is in base-70. Converting to decimal to see what it is:
3313×1657=5489641

Interestingly, 3313 is the Star of David figurate formed from combining two 70th triangles (2485 dots each). The 70th triangle is a very important creation number. It is the inner triangle within the 73rd triangle (of 2701 dots and holds the vessels of creation, see section 6 days and Sabbath footnote 1).
5489641 is the 3313th Triangle number and it is the base for Star of David 7319521 = 913×8017 (913 is the Gematria of Bereisheit). This needs further investigation.

The next solution found is in base-73. Converting to decimal to see what it is:

3601×1801=6485401

3601 is a very important creation number. It is the Star of David figurate formed from combining two triangles of size 73 (2701 dots each) and 6485401 is the 3601th triangle number. Thus, in the wisdom base, i.e. base-73, the solution is the Star of David formed from the merging of two triangles of 2701 dots each.

The next solution is in base-91. In decimal it is 5581×2791. Yes, 5581 is a Star of David number and also the 737th prime. This needs more investigation. I scanned up to base-136 and there were more solutions, all of whom were Star of David numbers.

We are seeing a pattern, every solution is a triangle number and the larger number is a Star of David number (made by combining two triangles of that particular number base (ex. base-73 solution is Star of David formed from two 73rd triangles). Thus, the solutions to the supreme symmetry are all directly related and point to the Star of David. Hence it seems there is a simple mathematical reason for these symmetries. But nevertheless, the fact that these solutions are related to Genesis 1:1 is significant.

So is there anything unique in 37×73, the base-10 solution? Yes! Both primes 37 and 73 are each solutions to the supreme symmetry in base-7 and base-10 respectively and both are Star of David figurate numbers. Another uniqueness, 2701 = 37×73 is a star of stars figurate number. It is unique and shiny out of all these special, star numbers. A star of stars whose stars follow each other and are center points of each other (see section "Geometric properties"). Another uniqueness: 2701 collapses to 2+701=703 in sum of thousands and 703 is the inner triangle of 2701. This has special significance and works out only in base-10.

Thus 2701 isn't just "rare" there are no other numbers like this at all in ANY number system.
(keep in mind, figurate numbers are geometric representation of numbers using dots. Thus, they are a way of representing numbers independently of any numerical system or base - an absolute way to represent numbers). return to text

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