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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).

prime numbers

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

repeating patterns

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.)

prime and non-prime numbers

All even numbers represent grid lines. Imagine opposite sides of a zipper, odd and even numbers.

twin prime sets

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

intervals of 6

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)

3-frequency

5-frequency

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

electromagnetic spectrum

Chart B shows twin primes, and the lines separating them suggests to me 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!

sequential frequency waves

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!

1- frequency wave

The #1- frequency wave includes all of the numbers on the strip, 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.

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)

The frequencies contain many interesting patterns

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.

wave segments

wave segments 2

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".

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.

spacing ratio

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 12-52-72-112-132-172-192-232- 252 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, 252 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 492 for example.

ratio points

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

strip board

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.

3 frequency

Begin by placing the #3 frequency on the #1 board,
which fills in all of the non-prime numbers to 25 (52).

5 frequency

The #5 frequency fills in the non-prime numbers to number 49 (72),
leaving only prime numbers marked as orange.

7 frequency

Frequency #7 to 121 (112)

11 frequency

Frequency #11 to 169 (132)

13 frequency

Frequency #13 to 289 (172)

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 (52) enter frequency #5, at number 49 (72) 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.

predictable intervals

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)

This primes-board represents a line of sight looking out into the universe. Imagine standing
on a spot about 13.9 Billion years out from 0 (the peg), where from that position looking out into
the universe (always away from center), 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.

Riemann zero line

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)

9.5 degrees

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!

zero point

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

beginning and end

You can see from the strip board pin (zero point), and this example of six frequencies (section 7 to 17),
that all of the frequencies emanate from a single source point! Therefore, section 7 to 17 as the start
of those 6 frequencies, and section -17 to -7 mirroring those frequency waves, occur simultaneously.
This idea is described as a reversal point.

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 Origin 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)

origin

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

spiralling dna model

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

melodic language

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

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

nine squares

To summarize all of the above information: 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 heart shape cut out of a piece of paper leaves an inverse cut-out pattern.

This next section contains additional ideas:

Golden ratio spiral

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.

prime spiral

Connecting the numbers in 2-d belonging to each frequency as was explained earlier:
Prime #1= 1-3-5-7-9-etc. #3= 3-9-15-21-27-etc. #5= 5-10-15-25-35-etc. #7= 7-21-35-49-63-etc. etc.
With the two-opposite spiral motions and 3-d view, it would be like looking into a kaleidoscope.

Twin prime frequencies such as 11 and 13 have a relationship because they exist next to each other.
Observe the mirror image qualities (shown earlier) of twin prime frequency patterns as they emanate
from, or intersect the zero point, just like a mirror's reflection.

pattern forming

primes sieve

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 zero point, and the source of light.

The top 1 small square represents the main square (grid paper) 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 and who knows how often.
With this information, try imagining the numbers as representing stars, the grid paper space or the
universe, and the idea of identical and perhaps finite universes.

Keep imagining 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. To repeat, 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 the #3 and #9 lines is 26.565°. It is also the passageway angle within the Great Pyramid.

An exact angle of 21.9911...° (Π x 7), yields perfect ratios in the prime sieve by creating a constant
ratio triangle. And section length A divided by B = 6.3, C divided by D = 2.1, and 6.3 divided by 2.1 = 3
This pattern is identical to the Stonehenge, Hunnebedden and Great Pyramid π pointer lines.
Question: How far out will the blue π line hit a horizontal/vertical grid point dead-on, if at all?

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.

right-angled triangle

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 only.

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! To repeat, the 1 small square in the upper left corner represents the entire main square
(grid paper), or universe however large it may be, and it also points to the idea of identical universes.

regular pattern 888

With this basic information showing an indefinite and regular progression of eight, the successive
hypotenuses can be determined without much effort for however long one wants to work on this:)

regular patterns

Counting grid squares to show yet another regular and consistent pattern.

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”.

To DNA and Prime Numbers

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