Exponentiation Zones (31-36)
This section is referring to wiki page-4 of zone section-4 that is inherited from the zone section-zones by prime spin-19 and span-exponentiation with the partitions as below.
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Background of exponentiation
In the standard (Mispar hechrechi) version of gematria, each letter is given a numerical value between 1 and 400, as shown in the following table. In the Mispar gadol variation, the five final letters are given their own values, ranging from 500 to 900.
Δ prime = 114th prime - 19 = (6 x 19)th prime - 19 = 619 - 19 = 600
Sub | i | β | f
=======+====+=====+======= === === === === === ===
1:1:0 | 1 | 1 | 2 {71} 1 1 | | | |
-------+----+-----+------- --- --- | | | |
1:2:1 | 2 | 2 | 3 {71} | | | | |
-------+----+-----+---- | | | | |
*1:2:2 | 3 | 3 | 7 = 1 + 2x3 | | | | |
-------+----+-----+---- | | | | |
*1:3:3 | 4 | 4 | 10 = 9 + 1 | | | | |
-------+----+-----+---- | | | | |
1:3:4 | 5 | 5 | 11 = 9 + 2 | | | | |
-------+----+-----+---- 9 1‘ | Δ100 |
*1:3:5 | 6 | 6 | 12 = 9 + 3 | | | | |
-------+----+-----+---- | | | | |
*1:4:6 | 7 | 7 | 13 = 9 + 4 | | | | |
-------+----+-----+---- | | | | |
1:4:7 | 8 | 8 | 14 = 9 + 5 | | | | |
-------+----+-----+---- | | | | |
*1:4:8 |{9} | 9 | 15 = 9 + 6 | | | | |
-------+----+-----+---- | | | | |
*1:4:9 |{10}| 10 | 19 = 9 + 10 | | | | |
=======+====+=====+==== === --- 1" --- |
2:1:0 | 11 | 20 | 20 = 19 + log 10¹ | | | |
-------+----+-----+---- | | | |
2:2:1 | 12 | 30 | 26 = 20 + 2x3 | | | |
-------+----+-----+---- | | | |
*2:2:2 | 13 | 40 | 27 = 26 + 1 | | | |
-------+----+-----+---- | | | |
*2:3:3 | 14 | 50 | 28 = 26 + 2 | | | |
-------+----+-----+---- | | | |
2:3:4 | 15 | 60 | 29 = 26 + 3 9‘ | Δ200 Δ600
-------+----+-----+---- | | | |
*2:3:5 | 16 | 70 | 30 = 26 + 4 | | | |
-------+----+-----+---- | | | |
*2:4:6 | 17 | 80 | 31 = 26 + 5 | | | |
-------+----+-----+---- | | | |
2:4:7 |{18}| 90 | 32 = 26 + 6 | | | |
-------+----+-----+---- | | | |
*2:4:8 |{19}| 100 | 36 = 26 + 10 | | | |
=======+====+=====+==== === --- --- |
*2:4:9 | 20 | 200 | 38 = 36 + log 10² | | |
-------+----+-----+---- | | |
3:1:0 | 21 | 300 | 40 = 36 + 2 x log 10² | | |
-------+----+-----+---- | | |
3:2:1 | 22 | 400 | 41 = 40 + 1 | | |
-------+----+-----+---- | | |
*3:2:2 | 23 | 500 | 42 = 40 + 2 | | |
-------+----+-----+---- | | |
*3:3:3 | 24 | 600 | 43 = 40 + 3 9" Δ300 |
-------+----+-----+---- | | |
3:3:4 | 25 | 700 | 44 = 40 + 4 | | |
-------+----+-----+---- | | |
*3:3:5 | 26 | 800 | 45 = 40 + 5 | | |
-------+----+-----+---- | | |
*3:4:6 | 27 | 900 | 46 = 40 + 6 | | |
-------+----+-----+---- | | |
3:4:7 |{28}|1000 | 50 = 40 + 10 | | |
=======+====+=====+==== === ==== ----
*3:4:8 |{29}|2000 | 68 = 50 + 3 x (2x3) {10³} Δ600 Δ300
=======+====+=====+==== Δ ====
3:4:9 |{30}|3000 |{71}= 68 + log 10³ ---------¤ Δ900
You may see this scheme is build by 3 (three) layers where the next layer will continue the primes object by carrying the tensor of prime 31 and 71 of previous layer. So it will return to the beginning position within 60+40=100 nodes per layer.
Relation to the primes
Let's combine them all then we will get 168 which is the total primes out of 1000 numbers. This 168 we will get it also when we combine the 1's and 17's cell of (31+37)+(35+65)=68+100=168.
The Ulam spiral or prime spiral is a graphical depiction of the set of prime numbers, devised by mathematician Stanisław Ulam in 1963 and popularized in Martin Gardner's Mathematical Games column in Scientific American a short time later.
Both Ulam and Gardner noted that the existence of such prominent lines is not unexpected, as lines in the spiral correspond to quadratic polynomials, and certain such polynomials, such as Euler's prime-generating polynomial x²-x+41, are believed to produce a high density of prime numbers. Nevertheless, the Ulam spiral is connected with major unsolved problems in number theory such as Landau's problems (Wikipedia).
According to the results of Princeton University USA in 1972, the distribution of the prime numbers shows in the Riemann zeta function between the position of its complex zeros and middle axis is identical with the rotation curve of energy distribution.
37 + 12 = 61 - 12 = 49 = 7 x 7 = d(13)
In the second opposing member, the position 19 in the second term gives a redundant value of the template 7 of 7 × 7 = 49. The opposite prime position 11 as a prime number is now forced to determine a new axis-symmetrical zero position.
Note that when 77 contains ‘Lucky 7 and 11' as prime factors it is also the product of the middle two numbers of this sequence (11*7 = 77) (Prime Curios!).
Subclasses of partition
When the subclasses of partitions are flatten out into a matrix, you want to take the Jacobian of each of a stack of targets with respect to a stack of sources, where the Jacobians for each target-source pair are independent .
It’s possible to build a Hessian matrix for a Newton’s method step using the Jacobian method. You would first flatten out its axes into a matrix, and flatten out the gradient into a vector (Tensorflow).
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By parsering π(1000)=168 primes of the 1000 id's across π(π(10000))-1=200 of this syntax then the (Δ1) would be initiated.