Basic Prime
Number 1
1. A prime number,
according to generally accepted definition, is divisible only by itself and by 1. Number 1 , however,
complies with both parts of the definition, which therefore makes 1 a prime number by NATURE.
But despite this, mathematic science today denies 1
its prime status, after consent had developed during the 20^{th}
century. But truth does not depend on human decisions: If 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". Obviously, for sheer undecisiveness, 1 must be carried along with the other two groups.
However, this appears unsatisfactory.
3. What seems necessary
is a change of perspective: the priority of definition should not lie with the
prime numbers, but the composite numbers which should be understood as
particular positions of multiplicative number series, starting with number 1: Any individual number occurring is to be defined
as single, for example, 5 is (1*)5. If it is doubled and trebled, it's 2*5 = 10 and 3*5 = 10.
The first part of the multiplication series should be 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 is multiplier
as well as multiplicand. In its first aspect
1 can be seen as a constant, and in its second
aspect all successive numbers as multiplicands in unmultiplied singleness: 1*1, 1*2, 1*3 …, 1*99 etc. As to number 1 the function of both multiplier and multiplicand
potentially 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:
A composite number consists of two or more factors greater than 1.
A prime number consists of its own single factor.
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 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