Basic Prime
Number 1
1. A prime number, according to
worldwide consensus, is a number greater than 1
that is divisible only by itself and by 1. That
excludes 1 as a prime number. But truth does
not depend on human decisions: Whether 1 IS prime or not, is a logical
and an ontological problem. In fact, according to Wikipediainformation 1 could be found in lists of prime numbers until 1956. It is to be
considered whether the current definition of prime numbers has the right logic
on its side.
2. The reason generally forwarded for
the exclusion of number 1 from the class of
prime numbers is that the factors of composite numbers would not be written
unequivocally as 2*3 for example, but also as 1^{(n)}*2*3.
So what happens is
that in order to make the definition of prime numbers as simple as possible,
number 1 must quit the field. In fact,
according to the prevailing definitions, there aren't just two, but three groups of numbers: "composite,
prime, and the unit 1". This makes things
complicated again.
3. What seems necessary is a CHANGE OF PERSPECTIVE: the priority of definition
should not lie with the prime numbers, but
the composite numbers. A composite number is
to be understood as a particular positions in a multiplication series, starting
with number 1: Any individual number is to be
defined as an individual, for example, 5 and it's 1*5. If it is
doubled and trebled, it's 2*5 = 10 and 3*5 = 15. The first factor of the multiplication
series is called MULTIPLIER, the second MULTIPLICAND. So 10
would be the second successive result in multiplying 5.
The multiplicator 1 is IMMANENT
to the initial multiplicand number and so need not be placed in front of it.
The basic number 1 itself can be multiplier
as well as multiplicand. As a multiplier it
occurs only once, and a multiplicand it is a constant
in successive groups of ones: 1*1, 2*1, 3*1. As
to number 1 the application of both multiplier
and multiplicand constitutes a SQUARE 1*1, and equal progression of multipliers and
multiplicands creates more squares: 2*2, 3*3
etc.
4. Composite numbers and prime numbers
consequently should be defined as follows:
A composite number
consists of two or more factors greater than 1
within an imaginal series of multiplication,
for example 3*5 from preceding 2*5 or 3*4. Its
result 15 can start another series of
multiplication with multiplicands greater than 1.
A prime number does not contain two
or more factors greater than 1. It is the
beginning of a multiplication series (1)*PN, 2*PN etc.
As the current definition of prime numbers is
inadequate, it has to be reformulated. The order should be composite numbers first and prime numbers second:

The new definition eliminates the
aspect of division as unessential.
5.
For
mathematicians numbers are a matter of axiomatic theory, i.e., they do not concern
themselves with the origins of numbers and their possible meanings and
structures. So it eludes their attention that the decimal system contains
innumerable wellordered proportions and relationships. What could be the sense
of two classes of numbers if there didn't exist a wise system of order. One
example is the composite numbers (CN) and
prime numbers (PN) of 113
in subsequent additions:
CN 



4 

6 

8 
9 
10 

12 

49 
PN 
1 
2 
3 

5 

7 



11 

13 
42 
49:42 = 7*(7:6) 
6:7 numbers bring about an inversive
relation of 7:6.
Without 1 no relation would be possible.
Furthermore, every NUMERIC
VALUE (NV) is matched by a FACTORAL VALUE
(FV). The relationship of the two values can be written as an equation: 6 = 2*3: NV = 6, FV = 2+3 = 5;
5 = (1)*5: NV = 5, FV = 5; 1 = (1)*1: NV = 1, FV = 1. Numerical
values and fact oral values of prime numbers
are identic. As to the numbers 113 the
following relations emerge:

CN 
sm 
PN 
sm 
GS 

NV 
4 
6 
8 
9 
10 
12 
49 
1 
2 
3 
5 
7 
11 
13 
42 
91 
FV 
4 
5 
6 
6 
7 
7 
35 
1 
2 
3 
5 
7 
11 
13 
42 
77 

48 
36 
84 
36 
48 
84 
168 

35:42 = 7*(5:6); 77:91 = 7*(11:13) 
The numeric sums (NS) + factoral sums (FS) of the 6 CN
and 7 PN are
equally 84. The NS+FS of the first
9 (49, 17) and the last 4 (1013) numbers are 84 (48+36;
36+48) again.
The total of numbers within the decimal system proves
to be a network of innumerable relations, which would seriously be impaired without 1 understood as prime number.
6.
On
an ontological level the FIRST of all
numbers is the origin of everything being. Among geometrical figures the CIRCLE symbolises eternity most clearly, which
gives everything created its own image. The circle can be subdivided by three
axes which can be completetd into a the hexagon and be extended to form a
hexagram containing two tetractys. A tetractys is an equilateral triangle
consisting of 1+2+3+4 points, wellknown
from the Greek mathematician Pythagoras. The entire figure of hexagram consists
of 13 points:

The 13 numbers are placed subsequently from top to
bottom. The inner and outer circle are in ratio 1:3. There are composite numbers (blue) and prime numbers (orange)
both on the 6 extension points and the 7 hexagonal points. It has to be examined what ORDER there exists between the two classes of
numbers.
To begin
with, the subsequent numeration in a symmetrical structure of points results in
a ratio 6:7 correspondent to the numbers in
both areas. So the two sums are 42+49. It
turns out that the NS of the composite and
prime numbers in both areas are divisible by 7:

extension 
sm 
hexagonal 
sm 
tot. 

CN 
9 
12 


21 
4 
6 
8 
10 
28 
49 
PN 
1 
2 
5 
13 
21 
3 
7 
11 

21 
42 





42 




49 
91 
The sum 42 of the 6
extension numbers is the same as the 7 prime
numbers between 1 and 13, and vice versa the 7 hexagonal numbers agree with the sum 49 of the 6
composite numbers.
Including
the FV, the results are:

extension 
hexagonal 



ZZ 
PZ 
sm 
ZZ 
PZ 
sm 
GS 
NS 
21 
21 
42 
28 
21 
49 
91 
FS 
13 
21 
34 
22 
21 
43 
77 

34 
42 
76 
50 
42 
92 
168 
76:92 = 4*(19:23) 
written:
September 2018