Evennumbered Distances Since the primes are all odd numbers, the distances between them (indicated "D") will all be even numbers. The primes will always be situated more or less symmetrically disposed around a central point
of reference.
(1) 

D2 

+(1) 

D4 

D6 

D8 

D10 

D12 

D14 

D16 

D18 

D20 

D22 

D24 

D26 

D28 

D30 

D32 

D34 

D36 

D38 

D40 

D42 

D44 

Lines Of The Table With The Centers Of Symmetry Between the Two Primes Using the first few Twin Primes as examples to get started (5 7, 11 13, 17 19) : if the distance is D2 (from 5  to 7 +), there will be a 6n Fence (F6) between them ; if the distance is D4 (from 7 + to 11 ), D6 (from 5  to 11  and from 7 + to 13 +), or D8 (from 5  to 13 +), there will be a blitzkrieg (8 9 10) between them ; if the distance is D10 (from 7 + to 17 ), D12 (from 5  to 17  and from 7 + to 19 +), or D14 (from 5  to 19 +), there will be a complete extermination at F12 between them ; if the distance is D16, D18, or D20, there will be complete exterminations at F12 and F18 ; if the distance is D22, D24, or D26, there will be complete exterminations at F12, F18, and F24 ; if the distance is D28, D30, or D32, there will be complete exterminations at F12, F18, F24, and F30 ; if the distance is D34, D36, or D38, there will be complete exterminations at F12, F18, F24, F30, and F36 ; if the distance is D40, D42, or D44, there will be complete exterminations at F12, F18, F24, F30, F36, and F42 .
Columns Of The Table With Their Alternation In the left column, only one distance can be used only once, since they are all from "+" to "". In the right column, only one distance (including D2) can be used only once since they are all from "" to "+". In the central column, the distances can be repeated or intermingled, the second Prime conserving the same sign. The right and left columns must thus constantly alternate, spinkled with Distances from the center column.
Testing a sample The sample chosen is from #9951 to #10000 in the series of Prime Numbers. Each Prime Number is subtracted from the following to establish the Distance (D) between them.
D6 

D4 

D24 

D24 

D2 

D6 

D4 

D38 

D6 

D10 

D12 

D2 

D12 

D4 

D20 

D22 

D12 

D2 

D10 

D6 

D18 

D42 

D12 

D2 

D6 

D12 

D22 

D14 

D10 

D6 

D6 

D2 

D10 

D18 

D14 

D4 

D26 

D16 

D12 

D8 

D18 

D4 

D2 

D10 

D8 

D6 

D4 

D6 

D6 

D6 

The Distances behave exactly as predicted with alternation between the right ( to +) and left (+ to ) columns, with occasional intrusions from the central column (D6 D12 D18 D24 D30 D36 D42).
Statistics for this sample
Distance 

Instances 

Ratio (%) 

D6 

11 

22 

D2 

6 

12 

D4 

6 

12 

D12 

6 

12 

D10 

5 

10 

D18 

3 

6 

D8 

2 

4 

D14 

2 

4 

D22 

2 

4 

D24 

2 

4 

D16 

1 

2 

D20 

1 

2 

D26 

1 

2 

D38 

1 

2 

D42 

1 

2 

Small Distances It is interesting to note that, even between these relatively large primes, the three smallest distances (D2, D4, and D6) are not only in the first places but occupy 46% (almost half) of the distances, with Twin Primes (D2) occupying 12%, a halfdozen of them.
The Density Of Primes The density of any span of primes could reliably and accurately be obtained by using the inverse of the average of the distances between them.
Establishing  or + By applying the indications of  and + associated with each Distance size, it is possible to establish the sign of each Prime Number, or, in other words, on which side of a 6n Fence it is: "" = 1 (below a 6n Fence), "+" = +1 (above a 6n Fence).
104179 + 

104183  

104207  

104231  

104233 + 

104239 + 

104243  

104281 + 

104287 + 

104297  

104309  

104311 + 

104323 + 

104327  

104347 + 

104369  

104381  

104383 + 

104393  

104399 + 

104417  

104459  

104471  

104473 + 

104479 + 

104491 + 

104513  

104527 + 

104537  

104543  

104549  

104551 + 

104561  

104579  

104593 + 

104597  

104623 + 

104639  

104651  

104659 + 

104677 + 

104681  

104683 + 

104693  

104701 + 

104707 + 

104711  

104717  

104723  

104729  

Observations There are approximately the same number of each sign, 28 primes are  and 22 are +. Another sample might offer different proportions. The D42 between 104417 and 104459 (third line) signifies seven complete exterminations, at F104418, F104424, F104430, F104436, F104442, F104448, and F104454, for which we could factor all the neighboring  and + exterminated neighbors. There will be a 6n Fence immediately above any  Prime and below any + Prime.
Conclusion
Whatever structure there might be in Primes will be observed in
Liberation 2 extermination procedures rather than in all the existing primes which are only victim survivors.
To Testing Another Sample
