Prime Numbers

[rr6]

http://www.factmonster.com/math/numbers/prime.html

2,

3,

5,

7...( first polygon that has irrational internal angles )
{... 7 * 11 * 13 = 1001 Scherazade 1001 Arabian Nights }

11,

13...12 equal radius spheres around and nuclear 13th gives us the Euclidean operating system of Universe, the Vector Equilibrium aka cubo-octahedron.

15, 17, 19, 23, 29,

31...stays prime number as it progresses outward to 7 places i.e. 33 33 33 1.
{ Pi^= 31.00 62 7.....}

37, 41, 43,

47 ..first prime beyond trigonometric function.

r6

[rr6]

Pi^3 = 31.00 62 7

31.00 62 7 66 80 29 98 201 7 54 7 63 15 06 7 10 1

See set of the 31 great circle-like planes( GrCP's ) of the 5-fold symmetrical icosahedron in link that follows.

http://www.rwgrayprojects.com/synergeti ... 5730b.html

31 doubled is 62 and that is the first set of two numbers after the double 00's on the irrational side of Pi^3.

3rd powering in math typically implies a 3D volume accounting. So 3rd powering of Pi gives a whole rational 31 followed by the irrational double zeroes which sets whole rational 31 even further from any counting sets of numbers on the irrational side and when we do get too the counting numbers it is 6 or 62 which is just the rational whole set of 31 doubled.

Here it is perhaps worthy to note, that, the 31 GrCP's come in both a left and right skewed versions when related to the left or right contractive infoldings of the 4-fold cubo-octahedron aka the VE or jitterbug. See following link.

http://www.rwgrayprojects.com/synergeti ... f6008.html

So the 31 GrCP's define 480 surface right-triangles and since we have left and right sets of the 480 that is total of 960 right-triangles.

After the 00 and 62 we come to number 7 and as mentioned previously, a heptagon( 7-sides ) is the first polygon to have irrational internal angles. There are is a list of sevens I can give that show seven as being a cosmic limit so suffice it to say, for me, I see 7 as a numerical cosmic limit of sorts i.e. in this specific Pi^3 set of circumstances, I see numerical 7 as representative of saying STOP here, or no need to go further with this never ending transfinite or is it infinite irrational number.

Although, the non-stable, 4-fold VE/jitterbug system is radially ergo diametrically slight larger than the 5-fold icosahedron, we still have to recognize that numerically speaking, 5( 5-fold ) is greater/higher and more complex than 4( 4-fold ) and in fact, within those 31 GrCP's we find 5 overlapping sets of the VE/jitterbug being defined.

Specifically it is the 10 GrCPs of the icosahedron that have the 5 sets of 4 GrCP's defining VE's. Sorry I don't have the link at hand that shows this clearly but can find it if any interest arises.

After 7 were back to a repeat of 6 and that 6 is doubled( twin/symmetry ) 33 and 33 instead of 31 and 31.

If we go on to the next set of 80, we then begin to think of the total set of primary cosmic great circle-like planes which is 87 i.e. the VE's 25 plus the left and right 31 totals to 87. So here again we encounter a seemingly cosmic 7 that we can conceptualy or virtually add to the 80.

However, of these 87, 14( 7 + 7 ) of them are congruent so that in effect leaves 73 primary cosmic GrCP's. So here again, if we take the 80 related to the 73 that is difference of 7.

I can find link to the 87 GrCP"s if there is interest.

R6

[Oschkar]

First of all, most of the properties you mention are dependent on our base-10 numeral system. If we used base 12, for example, pi^3 would look something like 27.00AA1A09, where A is a single digit for ten. The fact that 1001 is the product of 7, 11 and 13 is not really a coincidence: (x^3+1)=(x+1)(x^2-x+1). Then 1001 is the product of 11 and Ω1, where Ω is one less than the base. Then, in bases 7n+3 and 7n+5, Ω1 is divisible by 7.
(7n+3)^2-(7n+3)+1=
49n^2+42n+9-7n-3+1=
49n^2+35n+7=
7(7n^2+5n+1)

(7n+5)^2-(7n+5)+1=
49n^2+70n+25-7n-5+1=
49n^2+63n+21=
7(7n^2+9n+3)

A similar argument shows that Ω1 in bases 13n+4 and 13n-3 is divisible by 13, so... what you propose isn't really that remarkable.

[rr6]

There exists cosmic relationships that eternally inviolate. imho

All of this cosmic relationships can be expressed mathematically, and consistently, irrespective of base system of measure. imho

Within whatever base system of measure that is used, the inviolate cosmic relationship being expressed by that specific system of measure remains a constant and/ consistent. imho

http://en.wikipedia.org/wiki/Degree_(angle)
Unit( whole ) circle..."Another motivation for choosing the number 360 may have been that it is readily divisible: 360 has 24 divisors, making it one of only 7 numbers that have more divisors than any number twice itself Furthermore, it is divisible by every number from 1 to 10 except 7. This property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention"...

I forget what other base units of circle--- or sphere if an infinity of cirlces ---are used ex military transit I came across was divided into 400 + or - parts as the unit( whole ) circle.

The circle still has two equal halves, 4 equal parts etc...... irrespective of what base unit is used to subdivide the circle.

So it goes with polygons and polyhedral also if not even more so, because they can be defined by a finite set of vertexial crossings ergo a subsequent defined set lines-of-relationships between those vertexial crossings and subsequently defined set 2D surface openings. So these are eternally existent cosmic sets regarding space.

Irrrespective of the base unit number system used, their exists a constant and consistent relationship expressed by the numerical system being used to the eternally existent ergo cosmically/absolute truths.

I'm not expert in mathematics so I cannot speak to what numbers pop out when using other numerical systems i.e. if we change the given value of Pi then of course all of the values, powers then derive using Pi are going to be different than the values I have given, however, does not invalidate the values in any way, the values I've given. imho


R6

[rr6]

Also in regards to prime number 31 is that it stays prime as it progresses outward for its first 7 places.
33 33 33 1.

Just as the icosahedron has left and right set of 31 GrCPP's, the human nervous system has bilateral set---31 left and right ---of spinal nerves.

At the top-- or at least closer to brain ---of these 31 spinal nerves lies the brain stem and here we find 12 cranial nerves.

The 5-fold icosahedron, and the 4-fold VE/cubo-octahedron are both defined by 12 equal-radius spheres.
---------
Only three primary, symmetrical and structurally stable polyhedra of Universe

5/phi-fold symmetrical icosa(20)hedron
..{ 31 left and right GrCPP's set }...

4-fold symmetrical octahedron
..{ the octahedron and tetrahedron GrCPP's are part of VE/cubo-octahedrons 25 GrCPP's set }...
3-fold tetrahedron
-----------
1 + 2 = 3( prime )

3 + 4 = 7( prime )

5 + 6 =11( prime )

7 + 8 = 15( not prime so the above pattern stops after three iterations.

r6

Pi^3 = 31.00 62 7
31.00 62 7 66 80 29 98 201 7 54 7 63 15 06 7 10 1
See set of the 31 great circle-like planes( GrCP's ) of the 5-fold symmetrical icosahedron in link that follows.
http://www.rwgrayprojects.com/synergeti ... 5730b.html
After 7 were back to a repeat of 6 and that 6 is doubled( twin/symmetry ) 33 and 33 instead of 31 and 31.
R6

[rr6]

Pi^3 = 31.00 62 7 66 80 29 98 201 7 54 7 63 15 06 7 10 1

..{ 3rd powering = volume as cubing( xyx ) or tetrahedroning( ABCD ) in 3D }....

We start with set of two integers as the #31, so I continue this pattern two integer pattern on the irrational side.

Not sure whether I've covered the significance of #7 as it relates to #80 above and the cosmic, 87 primary, great circle-like polygonal planes( GrCPP's ).

The 4-fold VE has its 25 GrCPP's and the 5-fold icosahedron has its 31 left skew and 31 right skew GrCPP's, in relation to the VE, so the total of 25, 31 and 31 is 87( GrCPP's), however, since 14 of those 87 are congruent, it may appear that we only have 73 primary GrCPP's.

87 is seven more than the given 80, and 73 is 7 less than the given 80.

31.

.00--infinity? set doubled?Symmetry set? Isolates 31 from 62, 7 etc.......

62

7--- remember, a 7 sided polygon is the first polygon composed of irrational angles and there is many more cosmic circumstances of #7 terminality aspect/function.

66--33 doubled---symmetry as in 00 is a symmetry also.

80

29

98

201--the first set of 3 integers because of where the #7 falls into place.

7

54

7

63

15

06---so here is the first place where a 0 precedes a number, i.e. 80 is different from 08 as rational whole number set, so it may be that we should combine 06 to 15 and get our first 4 integer set( 1506 )as a whole number. H,mmmm?

7

10-1

We have 31 bilateral( left and right ergo 62 ) spinal nerves.

On top of those 31 is the 12 cranial nerves( see brain stem area )

We have 24 ribs enclosing heart( one or more of 12 cranial nerves ) and lungs.

31 is stays prime continually for seven places i.e. 3 33 333 1

The torus has cosmically finite mapping set as 7 distinct faces/polygons.( See Arthur Young )



R6

[rr6]

1 + 2 = 3( prime )
3 + 4 = 7( prime )
5 + 6 =11( prime
..stop....

7 + 8 = 15( not prime )

30 = icosa(20)hedron edges

24 = Operating System of Universe( OSU )-- i.e.24 edges of VE/cubbo-oct(8)ahedron ----

30 / 6 = 5
..30 + 1 = 31 primary great/equatorial bisecting planes of ico.......

24 / 6 = 4
..24 + 1 = 25 primary great/equatorial bisecting planes of the Ve/cubo-octahedral Operating System of Universe( OSU ).....

56 may relate to one of the more stable elements of iron(?).

r6