The six radii of a hexagon, are the geometric explanation of for the algebraic formula, n * 6, plus or minus 1 i.e. we see two raddii of primes { and nonprimes } on each side of the 6th radii. So that 6 * n plus or minus one. So my conjecture i nearly 90s was that all primes, except 2 and 3 fall on those two lines.
Four sets of this planar, hexagonal, Eucliden pattern define VE { Vector Vquilibrium aka four bisections of the cubo{6}octa{8}hedron
So concentric tori that maybe overlap?
0/1Frequency abstract great circle { tori } 1, 2p, 3p, 4, 5p, 6 ....so four of these
2F 7p, 8, 9, 10, 11p, 13p ....so four of these
3F 14, 15, 16, 17p , 18, 19p...so four of these
3F 14, 15, 16, 17p , 18, 19p...so four of these
.
4F 20, 21, 22, 23p, 24, 25......so four of these
..............................23p.......................................24......................................................
....................................17p............................18........................................................
.........................................11p...................12....................................................................
..................................................5p.........6....................................................................
.........22.........16.........10.......4.........O........1......7p......13p.........19p.....25 { 25 is Buckys numerical turnaround number as is 50 etc.
....................................................3p.......2p......................................................................
................................................9.....................8...................................................................
...........................................15................................14........................................................
......................................21..........................................20...................................................
None of my past toroidal considerations considered this type of concentriclike tori
My prime number pattern discoveries were expressed in two ways;
1} a set of four rows very similar to Arthur Young's { Bell helicoptorr } approach, but he began with number counting number, #1 and I began with noncounting number #0, and used four linear rows, See LINK to arthurs Reflexsive Universe ideas, but my explorations occurred before I read his stuff,
2} placing numbers in hexagaonal circle, with several sot of concentric like circles after each 6 numbers which led to my conjecture that I mailed to the magazines that all prime numbers except 2 and 3 fall only on two radii { radial lines }, that are on each side of a radii that has no primes. So the algebraic expression of that, n * 6 plus or minus one, is where all primes fall exeetp 2 and 3 along with other nonprimes.
1} So here is the first four line/level pattern discovery scenario I found for primes, and this is 10 years before I concoted the third scenario ivolving torus;
.0.......................................................6............................................................12...............................................................18.........................
.........1.....................................5p...................7p.................................11p................13p.....................................17p.................19p.....................
....................2p.................4......................................8...............10.........................................14...................16........................................20
............................3p.........................................................9...............................................................15............................................................21
2} was the hexagon with all primes except 2 and 3 falling on, only two radii, along with other nonprime numbers. I dont have a link and old web page I had for free showing that hexagon scenario, as that free web page went byebye a long time ago, h,mm first time Ive done this with texticonic charactors. Zero is the center and placing 2 and 3 aside you can begin to see the two radii of prime numbers, O, 1, 7p etc and O, 5p, 11p prime numbers.
..............................23p.......................................24......................................................
....................................17p............................18........................................................
.........................................11p...................12....................................................................
..................................................5p.........6....................................................................
.........22.........16.........10.......4.........O........1......7p......13p.........19p.....25 { 25 is Buckys numerical turnaround number as is 50 etc.
....................................................3p.......2p......................................................................
................................................9.....................8...................................................................
...........................................15................................14........................................................
......................................21..........................................20...................................................
3} so some ten years later, I got back into my 1st discovery above, and I followed one of Fullers ideas about things that turn themselves insideout, ergo I did it with four lines, and that led to whole lot of new possible scenarios involving tori and much more;
.........1...................................5p...................7p.................................11p................13p.....................................17p.................19p.....................


0.......................................................6............................................................12...............................................................18.........................
.............................3p.........................................................9...............................................................15............................................................21


....................2p.................4......................................8...............10.........................................14...................16........................................20I
The top line line/level I associate with the outer peak of positive curvature of a single torus 1, 5p, 7p etc and as contractive Gravity
The two middle lines I asscociate Observed Time ergo physical/reality as associated with sinewave /\/\/\/pattern ergo 0, 3p, 6, 9, 12, 15, 18 inside the tube i.e. Gravity and Dark Energy inverse from the peakofcurvature to create the sinewave pattern /\/\/\/ of reality inside the tube and for those like you have not read my findings before, all fermionic matter is based on 3, 6, 9 12 and there are 18 kinds of flavored quark and 18 kinds of flavored antiquark.
The bottom line above I associate peak of inner negative curvature of the same torus and as repulsive/expansive Dark Energy
No, I'm not saying the shape of Universe is a dynamically changing torus, I'm saying ever particle in Universe, except Graviton and Darkion is based on two or more interfering great tore. We just never see { quantize } the outer and inner peaks ergo Gravitty ( ) is Metaphysical3 { spirit3 } and Dark Energy )( is Metaphysical4 { spirit4 }.
The weak nuclear force is based on three particles W W+ and Zo. See this LINK and go about half way on page on left to these three.
Gluons mathmatically add to nine { 9 } flavors but only manifest as 8 particles. I dont fully understand that no matter how many times Ive read the explanations.
My whole Cosmic Trinity/trinary Oultine shows how its trinary turtles all the way to the microbottom. Arthur Young never expressed any of the above and he got stuck on cosmic seven all the way to the microbottom scenario
I hope that explains the basics of how I came to where I am, tho there is much more involved than Ive gone into above.