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Primes and Patterns

While visiting one of our local Garden markets on August 17, 2013, my brother lent me a DVD titled “The story of Math” by Marcus du Sautoy. The riddle of the primes captured my interest and several weeks later I had found answers, sieve methods for finding prime numbers, and a workable algorithm (series of steps) for identifying primes and patterns in their appearance among the whole numbers, as well as making the Riemann hypothesis connection (line of zero’s). I presented this on February 2014 at the Yukon College (YRC-dept.) Yukon Territory.

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.
As you will see there are undeniable patterns in the distribution of the primes.


Instead of looking for a pattern in the prime numbers I began looking for it in the non-prime numbers. Similar to the Australian aborigines who look for patterns in the spaces between the stars, instead of patterns in the stars!

After first lining up all odd and even numbers in this manner (Chart A), I noticed that the non-prime numbers contained a repeating pattern occurring at regular intervals of 6.
(Numbers colored blue and green are non-prime numbers and the prime numbers are displayed as orange.)

repeating patterns

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

repeating pattern

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. The vertical spacing's are added for easier viewing!

strip pattern

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



electromagnetic spectrum

From here I continued with 20 or so additional sequential frequency waves as shown on the large display board.
This strip (2-d) or tube (3-d), however long, represents the entire electromagnetic (EM) radiation spectrum!
Speed of light in a vacuum c₀ 186282.3970425...mps and zero gravity 186282.3970915...mps

nothingness of free space vacuum

Prime numbers are like the stars in the sky or the holes in Swiss cheese, and the stuff that surrounds them has the obvious and perfect patterns. Consisting of the electromagnetic spectrum frequency waves they are like finely woven threads of fabric, and represent space and time.

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 as the first few primes, cover most of the non-prime numbers on the entire strip.

The numbers belonging to frequency 3 as mentioned earlier, occur at intervals of 6. The number 5 frequency has intervals of 10, number 7 has 14, and 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.


So, the frequencies consist of non-prime numbers overlaying the #1 frequency “C” strip, thus sifting or separating out all of the primes. As the frequency numbers increase in size, meaning the very first number beginning each frequency wave after the zero point (represented by the red pins), their wave segments stretch accordingly. Furthermore, the frequencies and their segments, or wave sections (for lack of better terminology), match each other in specific ways. For example five #7-frequency segments equal seven # 5-frequency wave segments. Five #11-frequency segments equal eleven # 5-frequency wave segments. Seven #11-frequency segments equal eleven # 7-frequency wave segments. Etc.
The frequencies contain many interesting patterns!

wave segments

wave segments

I realized that by knowing the shape and arrangements of the frequency waves, one could 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:

pyramid strip

The ''pyramid strip'' as I named it, is an essential tool for determining where exactly and how far along the strip the various frequency insertion points are located, depending on the need to know the size of the numbers!
As you can see, the strip demonstrates how the pyramid stretches horizontally with very predictable increases, while the height of the pyramid does not change at all.

spacing ratio

As mentioned earlier, the number 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 bottom line numbers are used from here on in.
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.)
This bottom line runs along the strip at the same consistent level, 4 squares down and 3 up.

ratio points

Demonstration using the strip board (prime numbers are colored orange!). I made transparent strips for the first few frequencies that will overlay each other on the #1 frequency ''strip board''.

strip board

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

3 frequency

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

5 frequency

Frequency #7 to 121 (112).

7 frequency

Frequency #11 to 169 (132).

11 frequency

Frequency #13 to 289 (172).

13 frequency

Place frequency #17, and continue like this.

17 frequency

As you can see, 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 red "infinity"π line and a thought-provoking postulation by David.

Observe how the measurements for the stops along the strip-board increase at very predictable intervals. For example Red = 1”-3”-5”-7”-9”-etc, and green sections 1”-2”-3”-4”-5”-etc. (The paper strip has 4 squares per inch)

predictable intervals

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 taken from the “The story of Math” DVD)

zero line

The Frequency waves on my board are separated for display purposes, and the line of zeros appears to lie in a straight line. However, Riemann’s hypothesis and the question do all zeros lie along this straight line is wrong since straight lines or something truly flat cannot exist.

You can see from the strip board pin or ''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 frequency waves, and section -17 to -7 as the end of those frequency waves occur simultaneously, sort of like an image reversal through a lens. This idea is described as a reversal point.

Where waves coincide/interact the phenomenon is called superposition. These wave interactions, particles of information called photons perhaps, exist as opposites but act in synchronicity with each other.

beginning and end

The distance that the 6 frequency waves (7 to 17) have to travel 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)


The distances increase like ripples in a circular pond for the subsequent wave sections such as 19-29, 31-41 etc.

Known in quantum physics and depicted in this diagram you can see how an electron and its inverted partner, irrespective of distance react simultaneously, and where the point of origin or zero point represents the past, present, and future existing simultaneously! For more on this idea see animal migration page.

Prime numbers are like the stars in the sky or the holes in Swiss cheese, and the stuff that surrounds them has the obvious patterns. Consisting of the electromagnetic spectrum frequency waves they are like finely woven threads of fabric, and represent space and time. Put another way, prime numbers are the musical notes, and the non-prime numbers describe their vibrational wave patterns in a very exact and predictable manner.
To know the note you must first hear the sound!

Compare the vertical sections such as section 7 to 17 on the strip, with the separated frequency line layouts on the board. Notice 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”. For example, 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 an angle of 18.4°. The triangle it forms consists of angles 90°, 71.6°, and 18.4°. The # 1 strip "C" correctly displayed below without the vertical spacing's, forms a triangle of 90°, 80.5°, and 9.5°.

9.5 degrees

When those measurements 3", 6", 9" etc. beginning with section 7 to 17 are transferred to the strip, the numbers they fall on starting from the zero point will be 72, 144, 216, 288, 360, etc. Again when correctly displaying strip C (Frequency #1) without the vertical spacing’s as shown here, the measurements are 1.5", 3", 4.5", etc.

zero point

spiralling dna model

The image presents the frequencies in a more realistic representation as circular or spiralling, instead of flat and straight, and it explains the 9.5° angle. This idea continues in the DNA and Primes page.

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

Additional ideas and questions that came to mind while working on this material:

pattern forming

primes sieve

prime sieve perfect ratios

hypotenuse squaresThe top corners for each square, representing frequency numbers 9, 15, 21, 27, etc. are evenly spaced as indicated by the black dots, and as you can see in the diagram, all the other squares have similar arrangements.

right-angled triangle

regular pattern 888

regular patterns

Here I counted grid squares to show yet another regular and consistent pattern.

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.

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”.

The amazing design and geometric precision in the distribution of the primes is such a Work of genius, that it should convince us that a supernatural intelligent Creator created this, and not a chaotic and ongoing “Big Bang explosion” out of which came perfect designs!

To DNA and Prime Numbers

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