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Is one prime?

One is the first positive number of the set of natural numbers, before 1, there was nothing, it is the only one that is truly indivisible, except by itself. The set of prime numbers greater than 3, begins its distribution with 1, not with 2 or 3; which are the only prime numbers, which are not of the form 6n+-1, yet they are considered prime, while they are not part of the set of 6n+-1.

The 1 is the first 6n+1, with (0) of value for (6n+1), the whole organization of natural numbers and prime numbers depends on it, it is the base on which everything rests. You can’t imagine the importance of 1! It is the heart of the system. It is the centerpiece of the construction of the building, while 1 is not considered a prime number, it is in my humble opinion an aberration, it would be high time? that 1 regains its former letters of nobility from the time of Euclid, of Pythagoras from the time when 1 was considered Prime. I think that an update of the definition of prime number is necessary.

That said, let’s see why 1 is the 1st of the prime numbers:

We can see in table 1 above, the relationship that links 1 to the prime numbers, without the 1, no 6 n+-1

Description of table 1:

The distribution of prime numbers, is characterized by the value of the intervals, which separates 1 from the 6n+-1, this value corresponds to « n+4n+2n », 4n and 2n, are the two reasons of all the sequences generated from 1, because 1 + (1×4) = 6n-1 = 5 and 5 + (1×2) = 6n+1= 7. Then 5 and 7 generate their own sequences and it is the same for all the 6n+-1.

Sequence of 1:

1+ (1×4) + (1×2) = 1 + 4 + 2   Development of the sequence of 1:

1 + 4 + 2 + 4 + 2 + 4 + 2 + 4 + 2 + 4 +….etc. Results 1; 5; 7; 11; 13; 17; 19; 23; 25; 29; 31….etc.

Sequence of 5:

5 + (5×4) + (5×2)= 5 + 20 + 10   Development of the sequence of 5:

5 + 20 + 10 + 20 + 10 + 20 + 10 + 20 + 10 + 20 + 10 + 20 + 10 + 20….etc. Results: 5; 25; 35; 55; 65; 85; 95;…..etc.

Sequence of 7

7+7×4+7×2= 7+28+14   Development of the sequence of 7:::

7 + 28 + 14 + 28 + 14 + 28 + 14+….etc. Results: 7; 35; 49; 77; 91; 119;…..etc

In the representation of the set of 1 above, in the first horizontal line, we see that 1 generates the sequence of 6n+-1 and 1 is the first term and the reason for this is: 4×1 + 2×1, which corresponds to the sequence: 1 + 4 + 2 + 4 + 2 + 4 + 2 …..∞… It is the same for all natural numbers, because

n + 4n + 2n is the link, which connects the integers to the 6n +- 1.

The tables stop voluntarily at 10, but they can be extended to infinity.

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