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Chapter 1 of Prime Technology

We use the function of complementary DNS from molecular biology and the

Mathematical Elementary Cell 30 "MEC 30".

In connection with the 275 year old idea of Christian Goldbach.

The complementarily arranged Mathematical Elementary Cell 30

In the formula, the MEC30 / 2 refers to the complementary system found in DNA (molecular biology), so we calculated the electrons in the base pairs.


Next we calculate, with the system, the number and positions of the primes. Through the exact description of the positions, we calculated the number of prime-number pairs, which has an even numbers, Goldbachsche conjecture.


The complementary principle is the operating system of the primes. Thus the basis for a quantum computer, it forms the mathematical way to logic of entanglement of the spin of elementary particles. As with electrons and photons. Which was described in physics as a ghostly appearance.


We show that with the "MEC 30" all properties of the primes are calculated. Thus also the assumption of Christian Goldbach: That every even number, which is larger than 2, consists of the sum of two prime numbers.
This "simple" guess of Mr. Goldbach contains two very good ideas. On the one hand, the number system controls and compares itself. On the other hand, the complementary principle of DNA can be found again. And in a simple graph, with the example number 60 very well represent.
The 60 consists of two 30s modules the "2 x MEC 30". Sharing by 2 of the number 60, is now graphically to show as a convolution. From 0 to 30 to the right and complementary from 30 to 60 to the left.

Red are the pairs forming positions that can not be divided by 2, 3, 5. In these red 8 pairs are only the 6 Goldbach pairs of the even number 60.


If you increase the even number 60 to 62, the opposing 30s modules in the convolution shift to the smallest possible pairing from 8 to 3 pairs.

Red are again the forming positions, in this shift, only 3 red pairs in the opposite 30s module are possible, but with 2 Goldbachpaaren 19 + 43 and "31 + 31" the even number 62 (without 2, 3, 5).


We increase the even number to be examined, in the convolution, from 62 to 90. Thus, the system shifts back to an even number that has to be divided by 30, such as 60, 90 or 120. Thus, the convolution synchronizes and positions the 30s Module cyclically to the maximum 8 pairs of modules per 30 module opposite. The exact description in the 4th chapter of primes technology.

It is essential that we can first show that the 3-pairing per complementarily positioned 30-module represents the smallest possible pairing. So we can use the ln, the inverse of the Euler number e, to compute the least existing Goldbach pairs.


We show that every even number above 60 contains a prime in its root (without 2, 3, 5) that determines the minimum number of Goldbach pairs.


I describe here, with this formula sign gp, the minimum number of Goldbach pairs of an even number that confirms the Goldbachsche conjecture.


The graph shows the number of Goldbach decompositions of n (n = even number). gp (n) = the minimum number of Goldbach pairs shown in the red line calculated using our formula.

How does our formula work?

n = 200,372 = 1,049 empirically determined Goldbach pairs.

gp (n) is according to our formula 1,027.


We take the root of n to calculate the primes below the root.


For this we use ln, the inverse of the number of Euler e.


Now we calculate the primes with the basic idea of Carl Friedrich Gauss. The number of prime numbers is rounded up, 74 pieces, which are important for the minimum calculation of the Goldbach pair gp here. They now show up below the root.


Now we come to the core, which is not in any research literature, that primes do not arise, but reduce by your own products in the red positions. It follows that the 74 primes position their products to product pairs system fair and thus remain 5,479 primes symmetrically in the number strand the Goldbach pairs result. We will describe this principle in the course of the 5 chapters of this work.

Since these are pairs, Goldbach pairs, these primes must be divided by 2 to show the number of possible pairs of prime numbers.

It first shows the maximum convolution with the 8-pair formation per 30-module opposite. Now we reduce the maximum convolution from 8 pairs per opposite 30's module to 1 pair per module, to "342.25" pairs.

Since the number n = 200,372 / 30, with the remainder being 2 it, has the smallest possible pairing of 3 pairs per opposite 30's modulus. The thus system-compatible the minimum quantity of 1,027 gp Goldbachpaare possesses of n.

{gp | gp is the minimum number of Goldbach decompositions of n and indicates that the even number n satisfies the Goldbachsche conjecture (Goldbach pairs)}

That alone fulfills the Goldbachsche conjecture, which we still describe exactly in the 5 chapters.


Since every even number up to infinity has a checkered pattern, which represents which positions are positioned in pairs in the convolution described above, we call them icons. The even number to be examined is examined by means of modular 30, and the remaining value is used to determine the checkerboard pattern

(eg 62 / modular 30 = 2, remainder 2).

With this we have been able to form the active positions of the pairs. Thus, the remainder has 2 = 3 active positions for pairs.

As the 15 icons show, the icon 2 has 3 pairs of forming positions such as the icon 4, 8, 14, 16, 22, 26, 28. The Icon 10 u. 20 has 4 pairs of forming positions. The icon 6, 12, 18 u. 24 has 6 pairs of forming positions and the icon 30 is without residue and has 8 pairs of forming positions. At the same time, the icons show a complementary arrangement, which will still play a major role.

The even numbers in the lower red area of the graph show the gp underlying of the Goldbach pairs. These numbers have the property of having in Modular 30, the remainder 2, 4, 8, 14, 16, 22, 26, 28. Thus, the checkerboard pattern of the 3-pair formation per opposite 30er modular. Furthermore, their numbers, which move exactly in the red line, do not have a "prime divisor" larger than 2, 3, and the like. 5, (5 <prime divisors <√N) and show exactly the lowest gp base value.

Now we describe the other mathematical effects that cause Goldbach pairs to break up, as the graph shows. This also shows why the distinctive trail is created with its columns in the graph. This also means that the reversal effect below the gp base value is not possible

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© Achim Martin Frenzel Primzahlentechnologie 2008