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 non-primes } 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?
0/1-Frequency abstract great circle { tori } 1, 2p, 3p, 4, 5p, 6 ....so four of these
2-F 7p, 8, 9, 10, 11p, 13p ....so four of these
3-F 14, 15, 16, 17p , 18, 19p...so four of these
3-F 14, 15, 16, 17p , 18, 19p...so four of these
.
4-F 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 turn-around number as is 50 etc.
....................................................3p.......2p......................................................................
................................................9.....................8...................................................................
...........................................15................................14........................................................
......................................21..........................................20...................................................
None of my past toroidal considerations considered this type of concentric-like 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 non-counting 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 non-primes.
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 non-prime numbers. I dont have a link and old web page I had for free showing that hexagon scenario, as that free web page went bye-bye 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 turn-around 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 inside-out, 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 sine-wave /\/\/\/pattern ergo 0, 3p, 6, 9, 12, 15, 18 inside the tube i.e. Gravity and Dark Energy inverse from the peak-of-curvature to create the sine-wave 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 anti-quark.
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 Metaphysical-3 { spirit-3 } and Dark Energy )( is Metaphysical-4 { spirit-4 }.
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 micro-bottom. Arthur Young never expressed any of the above and he got stuck on cosmic seven all the way to the micro-bottom 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.
