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<<Previous: Breath of Life

Beyond Decimal

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)01234567891011
Binary (Base 2)0110111001011101111000100110101011
Base 3012101112202122100101102
Base 401231011121320212223

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).
 
703=19*37
בְּרֵאשִׁ֖ית בָּרָ֣א אֱלֹהִ֑ים אֵ֥ת הַשָּׁמַ֖יִם וְאֵ֥ת הָאָֽרֶץ
1998 703
Total=2701

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).

Beyond Bases 2-10

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

A scan of 2 million primes in bases 11-36 reveals an extra 3 solutions![1]

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".

Thus, it seems in some sense the entire number system is tuned around Genesis 1:1 (and "Yisrael").

To summarize the criteria of these "divine numbers"
  1. 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).  
  2. prime factors revealed when added to its own mirror reflection - ex.2701+1072=3773
     
  3. 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. There is for sure something going on there.. However, since it is chochma Eloki (divine wisdom), what you and I grasp is only a drop in the ocean and even less than this of what's really going on..

As to the significance of semi-prime numbers and midpoint symmetry, I asked Oren Evran, an Israeli genius and pioneer in this field. 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

More on 10

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 (and our solar system has 10 main bodies - sun+9 planets)

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

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