Central Prime
In this section we are going to observe yet another magnificent display of numerical balances in Genesis 1:1. This one is very beautiful in its consistency and perfection. Please fasten your seat-belts and go slow..As before, the Gematria of Genesis 1:1 is:
2701 = 37×73 (mirror reflection of prime factors)
Likewise the PRIME INDEXES^{[1]} are mirror reflective:
The 12th prime number is 37
The 21st prime number is 73 (note the mirror reflection in 12/21)
The CENTER WORD in Genesis 1:1 is: את
This word contains the first and last letters of the Hebrew alphabet. And in the Zohar on this verse:
"what is את?.. This refers to the Torah which includes the letters from Aleph (א) to Tav (ת) through which the Heavens and Earth were created" - (Tikunei Zohar, Tikun 51)
ת | ש | ר | ק | צ | פ | ע | ס | נ | מ | ל | כ | י | ט | ח | ז | ו | ה | ד | ג | ב | א |
את has the first and last letter of the Hebrew alphabet |
Notice that א and ת are MIRROR REFLECTIVE in their positions in the Hebrew alphabet^{[2]} (these mirror symmetries hint to many things such as the Star of David and its meanings).
את is also the shortest word in the verse and has no translatable meaning, hinting to the sublime nature of the Torah.
Center Word of First Verse | ||||||
בְּרֵאשִׁ֖ית | בָּרָ֣א | אֱ-לֹהִ֑ים | אֵ֥ת | הַשָּׁמַ֖יִם | וְאֵ֥ת | הָאָֽרֶץ |
913 | 203 | 86 | 401 | 395 | 407 | 296 |
Of the 7 word gematrias, 401 is the only prime number (prime numbers are divisible only by themselves and 1). This too hints on the Torah which is the Prime creation (see above Zohar).
Prime Factors
Every number is either a prime or has a unique "signature" of prime factors.The prime factors of the 7 numbers are:
913 | = | 11×83 |
203 | = | 7×29 |
86 | = | 2×43 |
401 | = | Prime |
395 | = | 5×79 |
407 | = | 11×37 |
296 | = | 2×2×2×37 |
Sum of prime factors:
11+83 +7+29 +2+43 |
+401 |
+5+79 +11+37 +2+2+2+37 |
Total Sum=751 |
Interestingly, the 37th prime number = 157 (=mirror reflection of 751).
(in many ways, Genesis 1:1 is built around the number 37)
Let us see if this symmetry persists
Balance of Prime Factors
Amazingly:11+83+7+29+2+43 | =175 |
401 | |
5+79+11+37+2+2+2+37 | =175 |
perfect balance of prime factor sums around את=401 |
175 | 401 | 175 |
Prime Factor Indexes
If we convert the primes to their indexes:11 is the 5th prime number
83 is the 23rd prime number
2 is the 1st prime number (1 is defined by mathematicians as being in a category of its own)
7 is the 4th prime number
etc.
Thus:
Prime Factor Indexes | ||||||
913 | = | 11×83 | = | 5th prime | × | 23rd prime |
203 | = | 7×29 | = | 4th prime | × | 10th prime |
86 | = | 2×43 | = | 1st prime | × | 14th prime |
401 | = | 79th Prime | ||||
395 | = | 5×79 | = | 3rd prime | × | 22nd prime |
407 | = | 11×37 | = | 5th prime | × | 12th prime |
296 | = | 2×2×2×37 | = | 1st prime^{3} | × | 12th prime |
The sum of the prime indexes BEFORE את=79th prime are:
(5+23)+(4+10)+(1+14)=57
The sum of the prime indexes AFTER את=79th prime are:
(3+22)+(5+12)+(1+1+1+12)=57
Thus, we have a perfect symmetry of prime indexes around the center word index את=79th prime=401
57 | 79 | 57 |
Keep in mind there is no logical reason whatsoever for prime numbers to be related to their indexes. Prime numbers are found by trial and error. There is no mathematical formula for calculating them.
To Summarize:
Sum of Left/Right prime factors | = | 175 | 401 | 175 | |
Sum of Left/Right prime indexes | = | 57 | 79 | 57 |
Amazingly, the reciprocals of these numbers gives:
1/175 | = | 0.0057.. |
1/57 | = | 0.0175.. |
Prime Factor Digital Roots
The prime factors of the 7 numbers and their digital roots are:913 | = | 11×83 | = | (1+1)=2 (8+3)=11=1+1=2 |
203 | = | 7×29 | = | (7) (2+9)=11=1+1=2 |
86 | = | 2×43 | = | (2) (4+3)=7 |
401 | = | Prime | = | (4+0+1)=5 |
395 | = | 5×79 | = | (5) (7+9)=16=1+6=7 |
407 | = | 11×37 | = | (1+1)=2 (3+7)=10=1+0=1 |
296 | = | 2×2×2×37 | = | (2) (2) (2) (3+7)=10=1+0=1 |
The sum of the prime digital roots BEFORE את
=2+2+7+2+2+7=22
The sum of the prime digital roots AFTER את
=5+7+2+1+2+2+2+1=22
Thus, we have a perfect symmetry of prime factor digital roots around the center word את=prime=401=4+0+1=5
22 | 5 | 22 |
Prime Factor Index Digital Roots
If we convert the primes to their indexes and calculate their digital roots:As before,
11 is the 5th prime number
83 is the 23rd prime number
2 is the 1st prime number (1 is defined by mathematicians as being in a category of its own)
7 is the 4th prime number
etc.
Thus:
Prime Factor Indexes Digital Roots | ||||||||
913 | = | 11×83 | = | 5th prime | × | 23rd prime | = | (5) (2+3)=5 |
203 | = | 7×29 | = | 4th prime | × | 10th prime | = | (4) (1+0)=1 |
86 | = | 2×43 | = | 1st prime | × | 14th prime | = | (1) (1+4)=5 |
401 | = | 79th Prime | = | (7+9)=16=1+6=7 | ||||
395 | = | 5×79 | = | 3rd prime | × | 22nd prime | = | (3) (2+2)=4 |
407 | = | 11×37 | = | 5th prime | × | 12th prime | = | (5) (1+2)=3 |
296 | = | 2×2×2×37 | = | 1st prime^{3} | × | 12th prime | = | (1)+(1)+(1) (1+2)=3 |
The sum of the prime index digital roots BEFORE את=79th prime are:
(5+5)+(4+1)+(1+5)=21
The sum of the prime indexes AFTER את=79th prime:
(3+4)+(5+3)+(1+1+1+3)=21
Thus, we have a perfect symmetry of the prime factor index digital roots around the center word את=79th prime =(7+9)=16=1+6=7
21 | 7 | 21 |
Notice also how all these numbers have digit root = 4. את is the 4th word in the verse.
751 | = | 7+5+1 | = | 13 | = | 1+3=4 |
175 | = | 1+7+5 | = | 13 | = | 1+3=4 |
175|401|175 | = | 1+7+5+4+0+1+1+7+5 | = | 31 | = | 3+1=4 |
57|79|57 | = | 5+7+7+9+5+7 | = | 40 | = | 4+0=4 |
22|5|22 | = | 2+2+5+2+2 | = | 13 | = | 1+3=4 |
21|7|21 | = | 2+1+7+2+1 | = | 13 | = | 1+3=4 |
The story is not over...
Alternating +/- Sum of Prime Factors
Amazingly, even the alternating +/- sum of the PRIME FACTORS are also perfectly balanced. Observe the amazing fact that the alternating +/- sum of the PRIME FACTORS point right back to the center word value and the only prime word value (401).
11 - 83 + 7 - 29 + 2 - 43 + 401 - 5 + 79 - 11 + 37 - 2 + 2 - 2 + 37 =401 |
Alternating +/- Sum of Prime Factor INDEXES
Incredibly, the exact same pattern is revealed within the PRIME INDEXES. The alternating +/- sum of the PRIME INDEXES of the Genesis 1:1 Prime Factors points right back to the PRIME INDEX of 401 (the 79th Prime = 401):
5 - 23 + 4 - 10 + 1 - 14 + 79 - 3 + 22 - 5 + 12 - 1 + 1 - 1 + 12 =79 The 79th PRIME = 401! |
Alternating +/- Sum of Prime Factors Before/After
This same alternating +/- PRIME FACTOR symmetry exists before/after the central 401 prime.The +/- sum of the prime factors BEFORE את=401:
11 - 83 + 7 - 29 + 2 - 43 =-135
The +/- sum of the prime factors AFTER את=401:
5 - 79 + 11 - 37 + 2 - 2 + 2 - 37=-135
Thus, we have a perfect symmetry of +/- prime factors around the center word את=401
-135 | 401 | -135 |
Alternating +/- Sum of Prime Factor INDEXES Before/After
Incredibly, the same before/after symmetry is revealed in the PRIME INDEXES.The +/- sum of the PRIME INDEXES BEFORE את=79th prime:
5 - 23 + 4 - 10 + 1 - 14 =-37
The +/- sum of the PRIME INDEXES AFTER את=79th prime:
3 - 22 + 5 - 12 + 1 - 1 + 1 - 12=-37
Thus, we have a perfect symmetry of +/- PRIME INDEXES around the center word את=79th prime = 401
-37 | 79 | -37 |
Reciprocals of Total Alternating +/- Sum
The total +/- sum of all the PRIME FACTORS before/after 401 is:
11 - 83 + 7 - 29 + 2 - 43 + 5 - 79 + 11 - 37 + 2 - 2 + 2 - 37 =-270 |
The total +/- sum of all the PRIME FACTOR INDEXES before/after 79 is:
5 - 23 + 4 - 10 + 1 - 14 + 3 - 22 + 5 - 12 + 1 - 1 + 1 - 12 =-74 |
Incredibly, these two numbers relate back to -37 and -135 through their reciprocals:
The RECIPROCAL of -270 = 1/-270 = -0.0037037037037.. (infinite repetition of 037)
The RECIPROCAL of -74 = 1/-74 = -0.0135135135135.. (infinite repetition of 135)
note: most of the above numerical balances were originally discovered by Leo Tavares^{[3]}.
Summary
Sum of all prime FACTORS | = | 751 | |
The 37th prime number | = | 157 | (mirror reflection of 751) |
Balance of Left/Right prime FACTORS | = | 175 | 401 | 175 | (mirror and 175 same digits as 751) |
Sum of Left/Right prime INDEXES | = | 57 | 79 | 57 | (mirror symmetry) |
1/175 = 0.0057.. and 1/57 = 0.0175.. | |||
Balance of Left/Right prime FACTOR digital roots | = | 22 | 5 | 22 | (mirror symmetry) |
Balance of Left/Right prime factor INDEXES digital roots | = | 21 | 7 | 21 | (mirror symmetry) |
+/- Sum of Prime FACTORS | = | 401 | (same as center word) |
+/- Sum of Prime Factors INDEXES | = | 79 | (79th Prime=401) |
+/- Balance of Left/Right prime FACTORS | = | -135 | 401 | -135 | (mirror symmetry) |
+/- Balance of Left/Right prime factor INDEXES | = | -37 | 79 | -37 | (mirror symmetry) |
Reciprocal of Total +/- prime FACTORS | = | 1/-270 = 0.037037037.. | (infinite 037) |
Reciprocal of Total +/- prime factor INDEXES | = | 1/-74 = 0.0135135135.. | (infinite 135) |
Let us now look at some various other findings related to the 401 prime...
Other - Multiples of 401
Word Gematrias | ||||||
בְּרֵאשִׁ֖ית | בָּרָ֣א | אֱ-לֹהִ֑ים | אֵ֥ת | הַשָּׁמַ֖יִם | וְאֵ֥ת | הָאָֽרֶץ |
913 | 203 | 86 | 401 | 395 | 407 | 296 |
Another interesting mathematical fact around the 401 prime is that all the other words in Gen.1:1 can be combined to form a multiple of 401:
395+407 | = | 401×2 |
913+395+296 | = | 401×4 |
913+913+203+395+395+395+395 | = | 401×9 |
913+913+913+86+395+395+395 | = | 401×10 |
These combinations do not exceed 7 numbers and Genesis 1:1 has 7 words.
Interestingly, even the ALTERNATING +/- SUM OF THE 28 LETTERS of Genesis 1:1 points back to 401.
The alternative +/- sum of the 28 letters in Genesis 1:1 =
2-200+1-300+10-400+2-200+1-1+30-5+10-40+1-400+5-300+40-10+40-6+1-400+5-1+200-90
= 2005 = 5×401 = (Small Gematria of את × Gematria of את)
This is interesting also because 5×401 reminds 5401, the same way that 2701 is related to 271, dropping the zero, or pushing the 1 with a zero. I already saw many cases where the breaking apart of digits and multiplication of those digits is part of the way the torah hints at numbers. 2701 is also the center point of 5401. This needs more investigation.
Other - Super Primes
As before, the center word in Genesis 1:1 is: את and contains the first and last letter of the Hebrew alphabet. According to the mystical writings, the verse can also be read "In the Beginning, G-d created את", i.e. the Torah which includes the 22 letters from Aleph (א) till Tav (ת) (see Zohar, Tikun 51). These 22 letters were the building blocks of creation. According to our sages, G-d first created the Torah and then afterwards used it to create Heaven and Earth.Interestingly, the 22nd "super-prime" number is 401.
"Super-prime" numbers are defined as primes whose index is also a prime number.
Here are the first 25 "super-primes":
# | super prime |
1 | 3 |
2 | 5 |
3 | 11 |
4 | 17 |
5 | 31 |
6 | 41 |
7 | 59 |
8 | 67 |
9 | 83 |
10 | 109 |
11 | 127 |
12 | 157 |
13 | 179 |
14 | 191 |
15 | 211 |
16 | 241 |
17 | 277 |
18 | 283 |
19 | 331 |
20 | 353 |
21 | 367 |
22 | 401 |
23 | 431 |
24 | 461 |
25 | 509 |
Interestingly, 401 is the 79th prime number and 79 is the 22nd prime number.
Other - 2701th Prime
An interesting symmetry of 2701:2700 | + | 2701 | + | 2702 | = | 2701×3 (nearby sum) |
2700th prime (24281) | + | 2701nd prime (24317) | + | 2702nd prime (24329) | = | 2701×3^{3} (72927) |
a scan of 100 million primes found that ONLY 2701 has this symmetry. Note that since 3^{3}=27, this can also be written as: | ||||||
2700th prime | + | 2701nd prime | + | 2702nd prime | = | 2701×(27×01) |
Another interesting mathematical property of 2701:
I ran a scan of one billion integers which are:
(1) mirror reflective and (2) center points of each other.
The results:
73,37
793,397
7993,3997
79993,39997
799993,399997
7999993,3999997
79999993,39999997
799999993,399999997
....
37 and 73 are the ONLY prime pairs in this series (and 2701=37×73).
Thus, it is all 7 then 9s then 3 and then reverse, so 37 and 73 are the KEY, prime units of this series and the rest are expansions.
Other - Mid-letter Symmetry
Let us now look at yet another layer of numerical symmetry.Word Gematrias | ||||||
בְּרֵאשִׁ֖ית | בָּרָ֣א | אֱ-לֹהִ֑ים | אֵ֥ת | הַשָּׁמַ֖יִם | וְאֵ֥ת | הָאָֽרֶץ |
14 letters | 14 letters |
14 is the Gematria of "Yad" (hand) in Hebrew, hinting G-d created the world with "2 hands", so to speak (i.e. the Sefirot of Chesed and Gevurah), as written: "My hand has laid the foundation of the earth, And My right hand has stretched out the heavens" (Isaiah 48:13)
Genesis 1:1 has 28 letters. Half of those (14) are in the first 3 words and the other half in the last 4 words. This splits the verse in half, revealing yet another axis of symmetry. There is also an "At-nachta" (pause) cantilation note at the 3rd word - "Elokim" which further confirms the split.
Let us examine the balance of words in this split.
Word Gematrias | ||||||
בְּרֵאשִׁ֖ית | בָּרָ֣א | אֱ-לֹהִ֑ים | אֵ֥ת | הַשָּׁמַ֖יִם | וְאֵ֥ת | הָאָֽרֶץ |
913 | 203 | 86 | 401 | 395 | 407 | 296 |
14 letters | 14 letters |
Multiplying the first half (first 3 words): 86×203×913 =15939154 |
|||||
digit sum | = | 1+5+9+3+9+1+5+4 | = | 37 | |
sum of hundreds | = | 15+93+91+54 | = | 253 | |
sum of thousands | = | 15+939+154 | = | 1108 | |
Multiplying the second half (last 4 words): 296×407×395×401 =19082162440 | |||||
digit sum | = | 1+9+0+8+2+1+6+2+4+4+0 | = | 37 | |
sum of hundreds | = | 1+90+82+16+24+40 | = | 253 | |
sum of thousands | = | 19+082+162+440 | = | 703 |
Notice how both halves share the same digit sum (37) and sum of hundreds (253).
Both 37 and 253 are important "Star of David" numbers - the 3rd and 7th stars respectively (=37)
The sum of thousands 703 is also an important number in Genesis 1:1 (and 703 = 37th triangle number).
According to Oren Evron, 1108 reduces to 1+108=109, a very important number and the gematria of עגול (circle) which refers to Pi. Interestingly, עגול has ordinal Gematria of 37 and small Gematria of 19, the two lower Gematrias of "wisdom". It also has triangle Gematria (mispar kadmi) = 457, the center point of the opening word Bereisheit. This needs more investigation.
Notice also: 2701 = 37 × 73 and 2701 + 1072 = 3773 (double symmetry)
27011072 = 2^{11} × 11^{2} × 109 (symmetry in 2^{11}/11^{2})
This too needs investigation.
Roshei Teivot (first letters)
Interestingly, the primes of the Roshei Teivot (first letters) also display this 3/7 relationship.
Roshei Teivot of first 3 words | ||||||
בְּרֵאשִׁ֖ית | בָּרָ֣א | אֱלֹ-הִ֑ים | אֵ֥ת | הַשָּׁמַ֖יִם | וְאֵ֥ת | הָאָֽרֶץ |
בְּבָּאֱ = 3rd Prime (5) |
According to the Zohar (Hashmatov Chelek Aleph, 251a) the Heaven and Earth were created by the Divine Name אֵ֥-הַוְהָ = 17.
This Divine Name is in the Roshei Teivot of the last 4 words:
Divine Name | ||||||
בְּרֵאשִׁ֖ית | בָּרָ֣א | אֱ-לֹהִ֑ים | אֵ֥ת | הַשָּׁמַ֖יִם | וְאֵ֥ת | הָאָֽרֶץ |
אֵ֥-הַוְהָ = 7th Prime (17) |
Thus, the Roshei Teivot (first letters) of Genesis 1:1 are split into 5/17. Interestingly, these are the 3rd and 7th prime numbers respectively (37).
note that symmetry is a sign of purpose and intent. If one were walking in the woods and he came across one or two symmetrical arrangement of stones in a triangle or star formation, he would immediately suspect that someone was there and arranged them in this formation with intent. (interestingly, we also find many displays of symmetry in the universe such as in the fundamental particles (ex.quarks) and their mathematical properties.)
>> Next: Star of David
Footnotes
- [1] the prime indexes can be checked at https://www.numberempire.com/numberfactorizer.php return to text
- [2] in the "At-Bash" reversal these 2 letters interchange return to text
- [3] he told me it is fine to use his findings provided he is cited as the discoverer return to text
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