## Primes and Patterns

Primes are the atoms and basic building blocks of mathematics. The challenge for hundreds of years

has been to decide whether a given number is a prime or not, and to find a pattern in the distribution

of the primes. I shared my ideas and findings February 2014 at Yukon College (YRC-dept).

Instead of looking for a pattern in the prime numbers, I began looking for it in the non-prime numbers.

When lining up odd and even numbers in this manner, I observed that

the #3 frequency contained a repeating pattern at regular intervals of 6.

Non-prime numbers are blue and green, and prime numbers are orange.

The spacings between the twin prime sets such as 11/13 and 17/19, consist of multiples of 3.

When lining up the sections ** horizontally**, a zigzag pattern forming a frequency wave and consisting

entirely of non-prime numbers became apparent, with numbers bouncing from

**3**to 9 to 15- etc. at

regular intervals of 6. The appearance of this strip pattern brought to mind objects such as, a ribbon,

**tube**, high-speed camera, movie filmstrip, and a railroad track.

*(vertical spacing's for easier viewing)*

The finding of #3-frequency, was quickly followed by the #5-frequency pattern.

Chart** B** shows twin primes, and the lines separating them suggests measured spectral rays

and time lines in the electromagnetic spectrum, which range from short gamma to long frequency

radio waves. The spacing’s between them are multiples of 3 and can be measured accurately.

From here I continued with 20 or so additional sequential frequency waves.

As the prime number values increase, new frequency waves are produced!

Non-prime numbers consist of electromagnetic spectrum frequency waves, like finely

woven threads of fabric, and prime numbers represent the spaces in that net or grid.

*Interestingly, while we in the west generally look for patterns in the stars,*

*Australian* *aboriginals* *look **for patterns in the spaces between the stars**.*

Prime numbers are like musical notes and non-prime numbers describe their vibrational wave

patterns in an exact and predictable manner. To know the note, you must first hear the sound!

The #**1** frequency wave includes __all____ of the numbers__ on the strip (tube), both prime and non-prime

numbers. All other frequency waves consist of non-prime numbers only, except for the very

first number beginning each prime frequency wave! Frequencies 3-5-7, the first few primes,

cover most of the non-prime numbers on the entire strip.
(All grid lines represent even numbers.)

(The #**1** ultra high frequency wave contains, or consists of, the entire EMF spectrum.)

The numbers belonging to the #3-frequency as mentioned earlier, occur at intervals of 6.

The #5-frequency has intervals of 10, number 7 has 14, number 9 has 18, and so on. As you

can see it increases by 4 each time. For example **3**-9-15…, **5**-15-25…, **7**-21-35…, **9**-27-45… etc.

*(when the vertical spacing's for easier viewing are eliminated, the increases are 2)*

As the frequency numbers increase in size, meaning the very first number beginning each frequency

wave after the zero point as represented by the red pins, their wave segments stretch accordingly.

Moreover, the frequencies and their segments or wave sections, match each other in specific ways.

For example, five #7-frequency segments = seven #5-frequency wave segments. Five #11-frequency

segments = eleven #5-frequency wave segments. Seven #11-frequency segments = eleven

#7-frequency wave segments. Etc. The frequencies contain many interesting patterns.

By knowing the shape and arrangements of the frequency waves, one can predict prime numbers a

million miles down the strip. Nevertheless, how to know exactly at which points along the strip new

frequencies are required, is explained with this important discovery, I willl call it the* "pyramid strip"*.

The *Pyramid strip* overlays the 'C' or #1- frequency strip. It determines exactly where,

and how far along the strip, the various frequency insertion points are located,

depending on the need to know the size of the numbers.

The pyramids stretch with predictable increases, while their heights remain unchanged.

Again, the #3-frequency covers all other related frequencies such as **9**-15-21-27-etc, so that after

the first small pyramid 1-**9**-25 no other pyramid peaks are required, and only the base line numbers

are used from here on. The spacing ratio for the bottom line is 1^{2}-5^{2}-7^{2}-11^{2}-13^{2}-17^{2}-19^{2}-23^{2}- 25^{2} etc.,

(4-2-4-2-4-2-etc). Alternatively as ratios 2-1-2-1-2-1 or **1-0-1-0-1-0** etc.

*However, 25 ^{2} and all*

*numbers that are part of the prime 5 frequency sitting on these*

*ratio points*

*could also be*

*eliminated, but the consistent 4-2-4-2-4 pattern would be lost.*

*This idea continues with the*

*next frequency number 7 and 49*

^{2}for example.

The pyramid's base line maintains the same consistent level, 3 squares up and 4 down.

To demonstrate how perfect and orderly the prime numbers (colored orange), are encapsulated,

carried and fit *untouched* between all of the frequency waves, I made a #1-frequency strip board

with all the prime numbers marked on it in their proper place, and transparent strips for the first

several frequencies that will overlay it.

Begin by placing the #**3** frequency on the #1 board,

which fills in all of the __non-prime__ numbers to 25 (5^{2}).

The #**5** frequency fills in the non-prime numbers to number 49 (7^{2}),

leaving only prime numbers marked as orange.

Frequency #**7** to 121 (11^{2})

Frequency #**11** to 169 (13^{2})

Frequency #**13** to 289 (17^{2})

Place frequency #**17** and continue like this.

It effectively separates and sifts out the prime numbers from the non-prime numbers.

Example: At number 25 (5^{2}) enter frequency #5, at number 49 (7^{2}) enter frequency #7, and so on.

Imagine a train moving along a train track and passing known and predetermined stops along

the way. At each stop a new frequency is engaged to cover all non-prime numbers on the strip

up to the next stop and ahead of the train. As the distances between stops increase continually

the train can speed up since there are fewer stops and frequencies required. Again, distance and

speed increases but the frequency numbers decrease. In other words, placing progressively longer

sections of track ahead of a faster and faster moving train.

Compare to the infinity π line and a thought-provoking postulation by David.

The measurements for the stops along the primes-board increase at predictable intervals:

Red = 1”-3”-5”-7”-9”-etc, and green sections 1”-2”-3”-4”-5”-etc. (The strip has 4 squares per inch)

Imagine this primes-board represents a line of sight looking out into the universe from 0 (the peg),

where from that position it appears to be expanding same as the prime numbers, at an increasing

but predictable rate. Logically, an expanding universe already consists of pre-existing ever-growing

numbers, frequencies, patterns, and primes.

What Riemann observed in his mathematics were the peaks and valleys of frequency waves with

a common line running through them, the *zero line*. (Image from the *The story of Math* DVD)

The Frequency waves are separated for display purposes, and the line of zeros lie in a straight line.

Compare the vertical sections such as section 7 to 17 on the strip below, with the separated

frequency layouts on the board. Observe how the frequency waves are shaped, and how the 6

frequency line sections merge to points on the left side of the so-called zero line. Those points

west of the zero line show-increasing intervals of 3”. E.g., frequency lines 11 and 13 merge at 3”

west of the zero line and lines 23 and 25 merge 6” west of the zero line. Connecting those points

on the left side of the zero line will produce a line intersecting with the zero line at **-6**, and

tapering away from the zero line at 18.4**°**. The triangle consists of angles 90**°**, 71.6**°**, and 18.4**°.**

*Again, to this point the vertical spacing's were added for easier viewing!*

The #1-Frequency __correctly__ displayed without vertical spacing's. (triangle = 90**°**, 80.5**°**, **9.5°**)

From the strip board pin *(zero point, "infinity")*, and this example of six frequencies (section 7 to 17),

it shows that all of the frequencies emanate from a single source reversal point!

Therefore, section 7 to 17 as the start of those 6 frequencies, and section -17 to -7 mirroring those

frequency waves, occur simultaneously.

*The simultaneous opposing positions between entangled quantum particles, i.e. particles of light.*

The distance the 6 frequency waves (7 to 17) are from the **O**rigin before they line up vertically like

they did at the start even though they are now inverted, is 382,882.5 mm x 2= 765,765 mm.

(Squares are 1 mm)

(The LCM is 7 x 9 x 11 x 13 x 15 x 17= 2,297,295 / 6= 382,882.5)

1 section - 11 x 13= 143 mm-----------x 5355= 765,765 (143 mm from point of Origin)

9 sections - 9 x 15= 135 mm-- 15 mm x 51051= 765,765 (15 mm from point of Origin)

1 section - 7 x 17= 119 mm------------x 6435=
765,765
(119 mm from point of Origin)

Like increasing ripples in a circular pond for the subsequent wave sections such as 19-29, 31-41 etc.

Frequencies accurately shown as tubular, circular and spiralling, instead of flat and straight.

And as conjectured earlier, the #1 ultra high frequency wave as represented by the tube

contains the entire EMF spectrum.

In Holland when someone dies, they have an interesting saying, "de pijp uit gaan".

Translated it says, "exiting the tube". Traveling from entry point to exit point and over again?

It seems so according to the mathematical model described here, because the perfect

arrangement of primes, non-primes and frequencies exist in this tubular model as shown.

Prime numbers, orange (3-d) and black (2-d), may represent a melodic language.

Perhaps one day prime numbers can be a method of advanced communication.

This idea continues in DNA and Primes.

With this discovery and by knowing the frequency patterns, it is possible to decode encrypted

numbers by finding the primes that created this number. Because without knowing the original

primes it is almost impossible to decode that number. Simply locate the encoded number on the

#**1**-frequency strip, and observe the prime frequencies attached to it. For example, the following

numbers are the product of two prime numbers:

Product Primes (frequency numbers)

15 = 3 x 5

77 = 7 x 11

221 = 13 x 17

To sum up, the first nine squares represent **all** of the prime and non-prime numbers.

The diagonal lines represent the frequencies as they cancel out all of the yellow non-prime

numbers, leaving only the red prime numbers.

Therefore, by knowing exact and predictable frequency patterns, mathematicians should

be able to find a formula to see whether a given number is a prime or not.

Non-prime number frequencies have patterns, therefore prime numbers have inverse patterns.

A shape cut out of a piece of paper leaves an inverse cut-out pattern.

__This next section contains additional ideas:__

__Prime numbers, the Golden spiral in 3-d, and where the 0 point represents the start and finish:
__

Looking into the *tube* or frequencies toward the zero point, is like looking into the

**Golden ratio spiral** with its excentric or concentric spiral motion, and is comparable to the

spiraling twist of DNA. The #1-frequency represents the entire golden ratio spiral, 1-3-5-7 etc.,

with each added frequency** **forming increasingly complex geometric and fractal like repeating

patterns. The 3-frequency makes ¾ turns 3-9-15 etc. *(Example section 9 to 15 in blue.)*

The 5-frequency makes 1-1/4 turns, 5-15-25 etc. The 7-frequency makes 1-3/4 turns, 7-21-35 etc.

__This next sieve method for finding prime numbers begins with several observations: __

The top row of numbers spaced at regular intervals of 6, (3 - 9 - 15 - etc.) represents the

#3-frequency wave's non-prime numbers as identified in my first sieve find.

Imagine the **O** in the top left corner as the point of Origin or "infinity", and the source of light.

The top 1 small square represents the main square (grid paper, "Universe?") however large it may be.

So when looking towards the point of Origin, or the top left corner of the small square,

it appears that this idea repeats itself going in both directions.

Imagine that the blue lines are light rays passing through the grid paper, which has pinholes

at the center of certain squares for the light to pass through. Again, the horizontal top row of

numbers 3-9-15-21-etc. through which the blue lines pass through first, are numbers belonging to

the #3-frequency wave.

None of the squares representing the orange prime numbers, is ever intersected dead center

by any blue frequency waves, only the non-prime number squares are, and so the prime numbers

(free-spaces) are free to drop out as in a Tetris game, down to the 45°- #3 diagonal line.

The angle between #3 and #9 lines is 26.565°. It is also the passageway angle within the Great Pyramid.

The top corners for each square, representing frequency numbers 9, 15, 21, 27, etc. are evenly spaced

as indicated by the black dots, and as in the diagram all the other squares have similar arrangements.

All expanding right-angled triangles originate from the *zero point* in the upper left corner.

Shown here are the first few right-angled triangles beginning the primes sieve.

__All__ triangles consist of non-prime numbers.

The first red right triangle 3² + 1.5²= 11.25 (A² + B²= C²), and so on.

The small orange triangle 1² + .5² = 1.25 is distinct from the others, because it resides **above**

all of the numbers! The 1 small square in the upper left corner is a copy of the entire main square

(grid paper) and so on.

With this basic information showing an indefinite and regular progression of eight, the successive

hypotenuses can be determined without much effort.

The material in this web-page may help to clarify other outstanding areas concerning prime

numbers such as the “*Twin prime problem*” and the “*Goldbach conjecture*”.