Chapter 4 of Prime Technology

In Chapter 4, we introduce the 15 complementary-structured ikons into the functional graphic by iteration. Thus we show the complete induction also for the Goldbach pairs.

This characteristic convolution of the even numbers is a fundamental test element in the numerically exact chart. A change of perspective to biochemistry helped in developing the idea of operating with opposed convolutions. So it happened that D.Sc. Beate Liebig (molecular biologist) and Achim Frenzel (project management) discussed the issue of specific convolution.

 

Biochemistry: RNA molecules show, in relation to their base sequence (positions), very specific convolutions leading to complex secondary and tertiary structures. Convolution plays an important role in all biologic systems, a fact from which we developed the idea that this fundamental system is reflected also in the order of numbers with the properties of position and information.

 

So we had presented the addition as folding.

Position identifier of the active prim positions, which can only form pairs in this convolution, per 30th module.

We fold the even number 60 over their "middle" 30 again

We called the positions the active prime positions opposite the fold.

For an even number to be divided by 30, as here the number 60, the 8 active prime positions are always in this combination.

These 8 active prime positions are shown in the MEC30² and can be represented as an ikon, so that results in this ikon in which all positions are active and marked in red.

 

The subsequent even number, such as 62, to divide by 30, with the remainder 2, shifts the larger convolution. So that only 3 pairs, active prime pairs per opposite 30's module can be formed.

Position identifier of the active prim positions, which can only form pairs in this convolution, per 30th module.

The 3 active prime positions are in the combination of these pairs

These 3 active primes position can now be entered in the ikon, so this ikon is created with the red marked

positions 1, 13, 19.

It follows that the MEC 30 with 15 even numbers also forms 15 convolution cycles.

With the modular 30 and the rest, it is now possible to assign any even natural number to infinity to one of the 15 positions and thus represent its specific convolution ikon.

 

In the ikons one can show that here too a complementary system is formed, a permutation with repetition. In the following graphic we show the interaction in a 30s cycle.

 

 

Graphic representation of the 15 cyclic folds and their ikons.

The graph shows which of the 15 specific foldings belongs to the even number. This also results in the associated ikon with the active primes positions.

 

 

 

Overview:

30s cycle of the 15 even number positions.

Every even number figuratively has a specific checkerboard pattern.

The number of active primes positions determined during folding is highlighted in yellow.

 

Now the specific icons can be entered by iteration into the functional graphics shown below.

It shows that complete induction is also valid for the Goldbach pairs.

Hence the cardinal statement for our theory:

The distribution of the primes and their products always follows the specifications of the MEC 30².

Conclusion:
Goldbach's guess led to the idea that the system is investigating itself.

This formula shows the maximum number of Goldbach pairs X.

This formula shows the minimum amount of gp Goldbach pairs for an even number n to be examined.

For the mathematical proof of Goldbach's conjecture, we used the full induction on the graph. What applies to the MEC 30 holds until infinity that any even number greater than 30 is at least the sum of two primes,

without 2, 3, and 5.

 

The solution idea is a product of natural science and not mathematics.

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© Achim Martin Frenzel Primzahlentechnologie 2008