Divine Symmetriesdivine symmetries in Genesis 1:1, Prime numbers, and Pi
The Torah opens with the second letter Beit - a letter symbolizing duality. It consists of two parallel lines and one connecting line. Beit is a summary of the whole Torah. The top line represents Heaven while the bottom line represents Earth. The connecting line is man's job to connect the two. This is the purpose of creation (Vilna Gaon).
The world was created with the Beit (Midrash Otyot d'Rabbi Akiva-Beit). Thus, we find duality permeates the universe at every level. In physics, we find every charged particle has a corresponding anti-particle with all properties reversed. All particles also have a mysterious dual wave/particle nature at the fundamental quantum level.
In our human domain we find most creatures, including man, have a mirror (bilateral) symmetry. Namely, the creature can be cut into two mirror image halves identical to our eye. Other examples of duality: male/female, sun/moon, good/evil, body/soul, Heaven/Earth, and many more. All this is the signature of the Beit.
The Beit also represents the second of the Ten Sefirot used to create the world - the Sefira of Wisdom. The 10 Sefirot (spiritual divine lights) were divided into two groups of 3/7. Let us examine if this signature of duality is reflected mathematically.
As before the opening verse in the Torah has Gematria of 2701.
|Gematria of First Verse|
The first example of duality is as we saw already:
- 2701 = 37 * 73 (mirror reflection)
- secondly, if we add 2701 to its own mirror reflection:
2701 + 1072 = 3773
The original 37/73 prime factors are revealed in this sum. (I tested the first 100 million+ numbers by computer and none other than 2701 have these two symmetries)
- Another symmetry: if we multiply the 7 word Gematrias:
=304,153,525,784,175,760 (huge number indeed)
Adding the groups of Thousands: 304 + 153 + 525 + 784 + 175 + 760 = 2701 (same as Gematria!) Adding the digit sum: (3+0+4)
= 73 Adding the second digit sum: (7) + (9) + (1+2) + (1+9) + (1+3) + (1+3) = 37 (again 73 and 37 the prime factors of 2701!)
G-d's NameInterestingly, the third and final digit sum is:
(7) + (9) + (3) + 10
+ (4) + (4) = 26 26 is the Gematria of G-d's Name, the Tetragramaton:
26 * 62 (mirror reflection) = 1612
and 1612 + 2161 = 3773 (remember these numbers)
Prime NumbersPrime numbers are prime basic structures of creation.
They are defined as numbers which cannot be divided by anything except 1 and themselves. Mathematicians categorize "2" as the first prime number (1 is in a category of its own. "2" is also the only even prime number, since all other even numbers are divisible by 2 and thus not prime).
Let us examine their mysterious connection to the Torah's opening verse.
(as before 2701 = 37*73)|
Here are the first prime numbers until 73 (see table on the left).
73 represents wisdom as we saw. Thus, 21 is also symmetrical with 73 in its Gematria meaning. For "Truth" and "Wisdom" are synonymous here.
אמת (truth) = 441 = 3*7*7*3 (note again the 37/73 symmetry)
Prime Numbers of Opening VerseObserve the following incredible perfection.
|Gematria of First Verse|
|Total = 2701 = 37*73|
|Prime Numbers of First Verse|
Total Sum = 2161st Prime (19013)|
2161 + 1612 = 3773
Note that there is absolutely no logical reason of any kind for prime numbers to be related to their indexes.
There is no mathematical formula for obtaining prime numbers. They are found by trial and error.
Hebrew AlphabetThe Hebrew letters are the "prime number" building blocks of creation.
In the Talmud: "Betzalel knew how to join the letters with which Heaven and Earth were created" (Berachot 55a).
Rashi comments: G-d created the world by joining the Hebrew letters in various combinations.
The Hebrew alphabet is composed of 22 letters and 5 end letters. The most symmetric way to arrange them is in groups of three letters. This arrangement is known as Ayak Bachar.
note that in this arrangement each group is a multiple of 37*3 (37=wisdom!). 37 is the only number with this sequential repetitive digit property.
|Hebrew Alphabet Groups|
|א י ק||=||111||=||37*(1+1+1)|
|ב כ ר||=||222||=||37*(2+2+2)|
|ג ל ש||=||333||=||37*(3+3+3)|
|ד מ ת||=||444||=||37*(4+4+4)|
|ה נ ך||=||555||=||37*(5+5+5)|
|ו ס ם||=||666||=||37*(6+6+6)|
|ז ע ן||=||777||=||37*(7+7+7)|
|ח פ ף||=||888||=||37*(8+8+8)|
|ט צ ץ||=||999||=||37*(9+9+9)|
Their prime number indexes are:
|Prime Numbers of Groups|
|Total Sum = 37073 (incredible!)|
Pi PositionsThe circle is the most prime geometric figure and is defined by Pi.
Indeed, the creation began as a "dot" and expanded out as a perfect circle (Etz Chaim 1).
Here are the first positions in Pi of the Hebrew alphabet groups.
(these and the primes discovered by Leo Tavares)
|Locations in Pi|
|"111"||first appears in Pi||:||153rd||digit|
|"222"||first appears in Pi||:||1735th||digit|
|"333"||first appears in Pi||:||1698th||digit|
|"444"||first appears in Pi||:||2707th||digit|
|"555"||first appears in Pi||:||177th||digit|
|"666"||first appears in Pi||:||2440th||digit|
|"777"||first appears in Pi||:||1589th||digit|
|"888"||first appears in Pi||:||4751th||digit|
|"999"||first appears in Pi||:||762nd||digit|
|Total Pi Locations = 16012 (+21061 = 37073)!!|
|First Appearances in Pi|
"111" appears starting at the 153rd digit|
"222" appears starting at the 1735th digit
etc. (see above)
Another (of many hints of Pi in the Hebrew Letters and first verse):
If we sum the inverses of all the Hebrew letters:
=3.14015 (within 0.046 percent of Pi - M.Glazerson)
|2701||=||37*73||note mirror symmetry|
|2701+1072||=||3773||note prime factors revealed|
|Words multiplied||=||2701||sum of thousands|
|Words multiplied||=||73,37||first and second digit sums|
|Third digit sum||=||26||26*62=1612|
|73rd Prime||=||21||12/21 mirror symmetry|
|212||=||441||144/441 mirror symmetry|
|1st verse Primes||=||2161st Prime||2161+1612=3773|
|Hebrew Pi Locations||=||16012||21061+16012=37073|
Other: as we will see, the first verse is symmetric around its last 2 words which have Gematria of 703 (same as the sum of thousands for 2701 and many other interesting things).
- as we will see 703=19*37 has the same double mirror symmetry as 2701=37*73 in the base 7 number system.
- The 37073rd prime = 441703 - (441="Truth" as above, 703=last 2 words).
- The number of integers between the 703rd prime (5303) and the 2701st prime (24317) = 2161st prime (19013) - same as the primes of the first verse!
- As before, the Gematria of G-d's Name is 26. 26*62=1612 and 1612+2161=3773
Center PointsCenter points are an important property in the Genesis 1:1 mathematical structure.
What is the center point of 2701?
1351 is the exact center point of 2701|
i.e. for 2701 dots, 1351 is the middle dot. Let us dig deeper..
676 is the exact center point of 1351|
Thus, the center point of the center point of 2701
= 676 = 262 (26 is G-d's Name)
This is also the final center point of 2701 since only odd numbers have center points.
How about 2161? What is its center point? (we have seen this number and its mirror reflection 1612 earlier)
1081 is the exact center point of 2161|
i.e. for 2161 dots, 1081 is the middle dot. Let us dig deeper..
541 is the exact center point of 1081|
Thus, the center point of the center point of 2161 is 541 = Yisrael (ישראל).
|2701||is the center point of||5401||(5401 is similar to 541)|
|271||is the center point of||541||(271 is similar to 2701)|
We will see this number 541 (Yisrael) pop up again in many interesting ways, be'H.
>> Next: Pi and Genesis
-  second digit sum means reducing the digit sum a second time as follows:
304=3+4=7, 153=1+5+3=9, 525=12=1+2=3, 784=19=1+9=10, 175=13=1+3=4, 760=13=1+3=4
thus 7+9+3+10+4+4=37 return to text
-  the mathematical facts on the prime and pi indexes were discovered by Leo Tavares. He told me it is fine to use his findings provided he is cited as the discover. return to text
-  Notice also, the difference between 2161 and 2701 = 540
And likewise, the difference between their reflections, 1612 and 1072 = 540
540 forms a Star of David figurate with 12 Triangles of 45 (Adam) around a center point. see end of section "Geometric Properties" return to text