The
4 x 32 Genesis 1:1 matrix or grid, shown at the end of this article, comprises
the 128 possible Hebrew word value combinations, using each value no more
than once in any combination and including the null case. The design of the
matrix and the order of generation of the combinations are based on the binary
system and this design is wonderfully encoded within the mathematics of the
verse itself.
The
only prime value 401, the middle, shortest and only untranslatable word is the
figure from which the design elements are deduced. To begin to understand this
it is necessary to show the many allusions to powers of 2 (and therefore the
binary code) connected with this word and its value together with its
connections to the prime factors of the verse total 37 and 73 and their prime
order numbers. With regard to the order numbers of the primes it must be
stated categorically that the Intelligent Designer behind the mathematics of
Genesis 1:1 makes it abundantly clear that the number 1 is considered to be
the first prime number. The following few paragraphs will deal with the
statements made in this paragraph.
401
is the 4th (2^2) word value comprising 2 (2^1) letters. The word
ends on the 16th (2^4) letter of the verse, the letter itself being
the 22nd (a double 2^1) in the Hebrew alphabet. The first letter is
the 4th (2^2) occurrence of that letter in the verse and the 2nd
letter is the 2nd (2^1) occurrence of that letter. The figure 401
has 2 (2^1) value digits, 4 (2^2) and 1 (2^0). The 2 (2^1) word values
following 401 sum to 2 (2^1) x 401 and comprise 8 (2^3) letters. The 2 (2^1)
word values preceding 401 also comprise 8 (2^3) letters. This 4th
(2^2) word is the 2nd (2^1) of only 2 (2^1) words which occur
within other words. There are 4 (2^2) combinations of 2 (2^1) or more values
that are multiples of 401. The difference in values between this shortest word
and the longest word is equal to 2^9 (913 - 401 = 512). The difference of
their digit sums is 2^3 (13 - 5) and the difference in their number of letters
is 2^2 (6 - 2). The sum of the number of their letters is also a power of 2
(2^3). The binary notation of 401 (110010001) comprises 4 (2^2) powers of 2:
2^0 + 2^4 + 2^7 + 2^8. Two (2^1) of the powers are powers of 2, 4 or 2^2 and 8
or 2^3. The digit sum of 401's prime order number (80) is equal to 2^3.
401
is the only figure of the word values to contain the binary
digits 0 and 1. These are both consecutive and in order and, just as 401 is
the middle word, these 2 digits are exactly at the middle of the
20 which make the seven word values. In both instances the digits occur for
the 2nd (2^1) time in this 4th (2^2) word value. This is
the only instance where 2 consecutive digits each occur for the
2nd time. The positional values of the these two binary digits are
10 and 11, both these denary numbers having the possibility to be read
alternatively as binary numbers and the only instance in the
range 1 - 20 where 2 consecutive denary numbers could also be
read as binary numbers. The digit 0 plus its positional value when read as a
binary number is 2^1 (0 + 2) and the digit 1 likewise when added to the binary
reading of its denary position is another power of 2 (1 + 3 = 2^2).
The
number of possible combinations including the null case of n
elements is computed as 2^n and therefore the number of
combinations of the seven Genesis 1:1 word values, using each value no more
than once in any combination, is equal to 2^7 or 128 and the number of value
combinations 127 (i.e. the null case excluded). In a random set of 127 values
we would expect 127 to divide by 1, 127/2 to divide by 2, 127/3 to divide by 3
and so on. The expected number of occurrences of multiples of 401 is therefore
127/401 or approx 0.3. However, given that we are looking specifically at 401
it is only fair perhaps to look at the 120 combinations comprising 2 or more
word values. Therefore the expected number of combinations being multiples of
401 would be 120/401 but this is still equal to approx 0.3 occurrences. In all
there are five combinations that are multiples of 401 including 401 and
however calculated this is at least 13x the expected rate which
is quite extraordinary. But even more amazing is the fact that these
combinations occur in arithmetic progression:
401 401
x 1 A
401
802 401
x 2 B
395 + 407
1203
401 x 3
A + B
401 + 395 + 407
1604
401 x 4
C
913 + 395 + 296
2005
401 x 5
A + C
401 + 913 + 395 + 296
The
letters A, B and C represent the three different bases that make up the five
combinations and it can be seen that these bases are, incredibly, in a geometric
progression:
A
401 = 401 x 2^0
B
802 = 401 x 2^1
C
1604 = 401 x 2^2
Because
these bases are in a geometric progression based on powers of 2 we can convert
the order numbers of the multiples of 401 to binary numbers and substitute the
1's (i.e. the powers of 2) with one or more of the three bases to form the
multiples of 401. With three elements there are in all seven possible
combinations excluding the null case (2^3 - 1 = 7).
| order number - denary |
order number - binary |
base(s) |
combination value |
combination value/401 |
| 1 |
001 |
- - A |
401 |
1 |
| 2 |
010 |
- B - |
802 |
2 |
| 3 |
011 |
- B A |
1203 |
3 |
| 4 |
100 |
C - - |
1604 |
4 |
| 5 |
101 |
C - A |
2005 |
5 |
| |
|
|
|
|
| 6 |
110 |
C B - |
2406 |
6 |
| 7 |
111 |
C B A |
2807 |
7 |
Only
the first five multiples of 401 occur in the 127 combinations because bases B
and C both contain the same figure 395, the fifth word value, and duplication
is not allowed. However, the above table adequately demonstrates the principle
of converting an order number to binary and then substituting the 1's with the
appropriate base to generate the order of the combinations.
By
adopting this system to produce the 127 Genesis 1:1 word value combinations
each of the seven word values is equivalent to a different base or element.
Significantly, the five multiples of 401 are generated in arithmetic
progression. It can be seen above that the bases are read in order from the
right and undoubtedly this is one good reason why the Hebrew language is
written right to left.
The
number of possible combinations is derived from 2^n and the order also based
on powers of 2, specifically the binary system. We might reasonably expect the
dimensions of the matrix to be based on powers of 2 also. Listed below are the
numbers of columns and rows that would provide a uniform display.
1 x 128 or 2^0 x 2^7
2
x 64 or 2^1 x 2^6
4
x 32 or 2^2 x 2^5
8
x 16 or 2^3 x 2^4
To
view all the combinations as clearly as possible on one page the most logical
format would surely be 4 columns by 32 rows. Designer '401' would seem to
confirm this or at least provide some clues. The sum of 401 plus its letter
positions in the verse (401 + 15 + 16) is equal to 432. In addition, 401's
word order number is 4 and the 32nd word by rotation or cyclically
is again 401.
The
sum of the squares of 401's letter positions 15^2 plus 16^2 is equal to 401
plus its prime order number 80. The 2 figures that surround 401 add to this
same figure (86 + 395 = 481). Notably this figure 481 is also equal to 37
times its order number 13. The sum of the word value digits to 401 is 37 and
the alternate addition and subtraction of these same digits is 13, the order
number of 37. There are in all 15 prime factors/primes derived from the word
values and, by rotation, the 37th is 401 and the 401st
by rotation is 37. These are the only prime factors of the 15 that complement
each other in such a manner. 401 is the designer prime of the Genesis 1:1
matrix and prime 37, as will be shown, confirms the design, thus the strong
bonding between these two figures.
When
the primes and prime factors of the composite numbers of the natural numbers
are alternately added and subtracted the only instance in the
whole integer series where the result is the same as the integer occurs at 37
with the exception of trivial 1 where no computation has occurred. The
sequence of the primes/prime factors of the Genesis 1:1 values is 11, 83, 7,
29, 2, 43, 401, 5, 79, 11, 37, 2, 2, 2, 37. The result of the alternate
addition and subtraction of these figures is 401, the only prime of the seven
word values 913, 203, 86, 401, 395, 407 and 296. Any notion that this is
merely coincidental is shattered when the order numbers of these fifteen prime
numbers are alternately added and subtracted for the result is the order
number of prime 401. Given the fact that the order numbers are linear whilst
the primes themselves are chaotic and therefore non-linear, this outcome is
quite extraordinary.
The
principle of alternately adding and subtracting figures is surely proved
worthy by the three examples already mentioned. Applying this principle to the
seven word values of Genesis 1:1 the result is 679. This figure is a 3-D
figurate star number and these 3-D star numbers can be computed using the
formula 2n^3 + 6n^2 + 5n + 1. The first few in the series are 14, 51, 124,
245, 426, 679 ... So this number has to do with stars and notably the two
prime factors of the Genesis 1:1 verse total, 37 and 73, are 2-D figurate
stars, the 2nd and 3rd in the series, derived using the
formula 6n^2 + 6n + 1. Observe that the first digit of 679 is 6, the order
number of 3-D star 679. The sum of the first 2 digits is 13, the order number
of prime 37, the 2nd 2-D star. The sum of all 3 digits is 22, the
order number of prime 73, the 3rd 2-D star. When 679 is divided by
37 the remainder is 13, the order number of prime 37 and when divided by 73
the remainder is 22, the order number of prime 73.
The
only Genesis 1:1 word value which can be expressed as the sum of multiples of
the two verse total prime factors is 913 which is equal to 1 x 37 plus 12 x
73. Note that the sum of the multipliers 1 + 12 is 13, the order number of
prime 37. The other prime factor 73 is a mirror image of 37 and the sum of the
mirror images of these same multipliers is 1 + 21 that equals 22, the order
number of prime 73.
The
three principal prime numbers in the mathematics of Genesis 1:1 undoubtedly
are 37, 73 and 401. Some almost uncanny relationships exist between these
primes and their order numbers. The sum of these primes (37 + 73 + 401) is 511
and the sum of their order numbers (13 + 22 + 80) is 115, the mirror image of
their total. The sum of the two verse factors (37 + 73) is 110. This figure is
the 80th composite number and the 80th prime is 401. The
110th (37 + 73) composite number is 145 and this figure is equal to
37 plus 73 plus their prime order numbers 13 and 22. The three order numbers
13, 22 and 80 all have prime factor sums equal to 13 (13 = 13, 2 + 11 = 13, 2
+ 2 + 2 + 2 + 5 = 13).
The
37th prime is 151 and the 73rd 359. In a factor analysis
of the 127 combinations the 37th prime occurs twice and the 73rd
once. The verse is split exactly with one of the two 37th prime
multiples and the 73rd prime multiple: 913
203 86
401
395
407 296. The numbers in bold type total 1,795 equal to 5 x 359 the 73rd
prime. The remaining numbers total 906 equal to 6 x 151 the 37th
prime. By rotation or cyclically, the 37th word value is 203.
Both combinations that are multiples of the 37th prime number
begin with this figure: 203
+ 401 = 604 and 203
+ 407 + 296 = 906. The number 203 is both the mirror image and a numerical
anagram of 302 equal to the 37th prime times 2, the number of
occurrences in the factor analysis. 73 is the mirror image of 37 and in
an anticlockwise direction from the last value, the 73rd word
value is 395. In reverse this is the first value of the combination that
is a multiple of the 73rd prime (395 + 401 + 86 + 913). This
fifth word value 395 is an anagram of 359 the 73rd prime. This
figure is equal to 359 x 1, the number of occurrences in the factor analysis.
So how does the number 37 confirm the design of the
matrix? Just as it is with 401, there are several more combinations having
a factor of 37 than would be normally expected. 127/37 is equal to 3.4 showing
that 3 or maybe 4 at most combination values having a factor of 37 would be
expected. However there are 23 in all, nearly 7x the expected rate. On any row on
the matrix where a multiple of 37 occurs, the other figures on the row are
also multiples of 37 and significantly there are no other rows
with each of the values sharing a common factor. In addition to this, the
rows containing multiples of 37 are symmetrical on the matrix. There are 3
corner values on the matrix, 3 being a triangular number. These 3 corner values
are, or relate to, the first 3 triangular numbers that are multiples of 37.
1998 is equal to 3 x the first triangular multiple of 37, i.e. 666. The number
703 is the 2nd triangular multiple of 37 and 2701 the 3rd.
The binary notation of 37 is 100101 and therefore the
37th combination is equal to 913 + 86 + 407, equal to 2 x 703,
the first figure relating to binary and the latter figure being the 37th
triangular number and therefore a multiple of 37. This latter figure is also
equal to the sum of the last 2 word values, 407 and 296, the only 2 figures
in the word values that are multiples of 37, and interestingly the sum of
their place values 6 + 7 is 13, the order number of prime 37.
THE
PRIME COMBINATIONS
There are in all 20 combinations that are prime and
these are highlighted in blue. Combinations that are prime between the rows
of multiples of 37, the rows highlighted in yellow, occur in the palindromic
format 2, 5, 6, 5, 2. In each column the number of prime value combinations
total 5, 7, 3 and 5. Read as the four-digit number 5735 this is a multiple
of 37 (x 155) and the prime factor sum of this figure is 73 (5 + 31 + 37).
The middle two digits of this figure are 73 and the sum of the primes in
these middle two columns is 12702. The highest prime factor is 73 (2x3x29x73).
With any multiple of 73 having more than 4 digits, a minus sign can be placed
between the fourth and fifth digits to give a new number divisible by 73.
In this case 1 - 2702 is equal to - 2701 and this figure is the verse total,
equal to 37 x 73. The digit sum of these primes in the middle two columns
is 147, equal to 7x3x7, a digital representation of the two Genesis 1:1
prime factors 37 and 73 overlaid.
Because there are 20 primes this means that there are
19 (the middle number between 1 and 37) adjacent pairs. The expected number
of adjacent pairs summing to a multiple of 37 would be 19/37. i.e. an expected
0.51 number of times, one at most. There are in fact 5 occurrences (nearly
10x the expected rate). Staggeringly the first
three of these pairs are all multiples
of 37. The first pair (401 + 487) adds to 888,
the Greek gematria of JESUS (see THE 20 PRIME COMBINATION VALUES OF GENESIS
1:1 table below). The average value of these three pairs is 1998, the gematria
of the first five words of Genesis, 'In the beginning God created the heavens'.
So indeed the first four primes sum to a multiple of
37. The first, middle and last groups of four primes also sum to a multiple
of 37. The total can be represented as 26 (Hebrew YHWH) x 592 (Greek GODHEAD).
The first, middle and last groups of twelve primes sum to a multiple of
37 and each of these groups of 12 are, individually, multiples of 37. The
middle 18 primes sum to the palindromic number 24642 and the average value
of these 18 primes is 37 squared. Importantly, this figure 24642 clusters*
to 666 (24 + 642). *I coined the word 'clustering' to mean replacing the
comma in any figure greater than 999 by a plus sign. As an example, the
Genesis 1:1 total 2,701 is equal to 703 when clustered (2 + 701). Any multiple
of 37 remains a multiple of 37 when clustered and in the case of Genesis
1:1 the total is the 73rd triangular number that when clustered becomes
the 37th triangular number, the order numbers of these triangular numbers
being the factors of Genesis 1:1.
Worthy
of note is the fact that there are two Genesis 1:1 values that are multiples
of 37. Two of the prime combinations have order numbers that are multiples of
37 and two of the primes plus their order numbers are also multiples of 37. If
1 is not counted as being the first prime number then none of the order
numbers of the primes would be a multiple of 37 and none of the primes plus
their order numbers would be a multiple of 37.
The
primes plus their order numbers that are multiples of 37 are the first and the last in
the series. The sum of all 20 primes plus the first and the last order numbers
is yet another palindromic figure 26862, a multiple of 37 that clusters to 888
JESUS.
The
highest prime in the series is 2017. This figure is an anagram of the verse
total 2701, an anagram of the number of value combinations 0127, and perhaps of greatest
significance, the order number of composite 2368, a multiple of 37 and the
gematria of JESUS CHRIST in Greek. The lowest prime 401
comprises the first and last letters of the Hebrew alphabet,
equivalent to the Alpha and Omega of the Greek.
The sum of the order numbers is 4284 and the sum of
primes 26542. The digit sum of these two figures is 37. The addition of
these two figures produces the number 30826, the prime factors being 2 and
15413 and not appearing to have any real significance. However, the difference
between these figures is 22258 that is a multiple of the 73rd
prime 359. On this premise the values of all twenty primes minus their order
numbers were calculated. The 37th combination of these figures is a multiple
of the 73rd prime and the 73rd combination is a multiple
of the 37th prime! The difference between these two figures is a multiple
of 37 and the prime factor sum of the 37th combination is a multiple
of 73.