About possible primes (Pp)
-
6n - 1
6n
+
6n + 1
Pp are always at a distance of 1 from a multiple of 6.
That is why we take multiples of 6 as a reference to identify Pp
We assign the notation to Pp in 6x - 1 "Ppa"
We assign the notation to Pp in 6x + 1 "Ppb"
...
...
6n
6
12
+
6n + 1
7
13
6n + 2
8
14
6n + 3
9
15
6n + 4
10
16
-
6n2 - 1
11
17
6n2
12
18
We can establish the types of numbers that may exist between two multiples of 6
Apart from possible primes, we always find two even numbers and one divisible by 3
That is, every integer is: Multiple of 6, Ppa, multiple of 2, multiple of 3 or Ppb
|
6n1
-
1
|
* |
6n2
+
1
|
= |
6n3
-
1
|
| 5 | * | 13 | = | 65 |
|
6n1
-
1
|
* |
6n2
-
1
|
= |
6n3
+
1
|
| 5 | * | 11 | = | 55 |
|
6n1
+
1
|
* |
6n2
+
1
|
= |
6n3
+
1
|
| 7 | * | 13 | = | 91 |
Application of sign law
This notation among possible primes gives us information about the characteristics of their possible products. Since they are multiplications, they follow the sign law
| 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 |
| Ppa1 | - | Npb1 | - | - | - | Ppa2 | Br | Ppb2 | - | - | - | Npa1 | - | Ppb3 |
|
+
|
-
|
-
|
| 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 |
| Npa2 | - | Ppb3 | - | - | - | Ppa4 | Br | Ppb4 | - | - | - | Ppa5 | - | Npb2 |
|
-
|
+
|
+
|
Relative bases
Np are also equidistant to multiples of 6.They do so as follows:
Br = 6 · Pp;
Ppa = 5, Npb1 = (6 · Ppa) · i - Ppa
Ppb = 7, Npb2 = (6 · Ppb) · i + Ppb
Ppb = 7, Npa2 = (6 · Ppb) · i - Ppb
Ppa = 5, Npa1 = (6 · Ppa) · i + Ppa
Ppb - Ppa = 2 => Npa1 = Npa2
Ppb - Ppa ≠ 2 => Npa1 ≠ Npa2
Npb1 = (6 · (6n1 - 1)) · i - (6n1 - 1)
i = Npb1 + (6n1 - 1) / (36n1 - 6)
Npa2 = (6 · (6n1 + 1)) · i - (6n1 + 1)
i = Npa2 + (6n1 + 1) / (36n1 + 6)
Npa1 = (6 · (6n1 - 1)) · i + (6n1 - 1)
i = Npa1 - (6n1 - 1) / (36n1 - 6)
Npb2 = (6 · (6n1 + 1)) · i + (6n1 + 1)
i = Npb2 - (6n1 + 1) / (36n1 + 6)