Discovering Zero Among the Prime Numbers

It was a big surprise discovering zero when I was really looking for prime numbers. Back in 1992, I had a simple computer at my disposal and assigned myself the task to find out what was going on with the prime numbers. It took some good detective work, but once that larger answer was known it was actually not a big deal. Yet there was a big surprise staring at me: Zero was a natural number.

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I found myself walking in the footsteps of Eratosthenes, the Greek polymath from North-Africa who created his sieve for finding prime numbers more than 2200 years ago. Following his sieve, there was no linkage between the prime numbers, though many patterns can indeed be discerned. Prime numbers have in common that they remain virgin numbers, are not divisible by any other natural number. Dividing a number by 1 is basically a moot division and if so desired it can be ignored.

As already shown with Eratosthenes’ sieve, the linkage of the prime-number phenomenon is found among the non-prime numbers; this action results in leaving the prime numbers untouched by division. It is not too dissimilar to bowling pins left standing after a player threw a couple of balls. Using a bowling term therefore, prime numbers are the ‘open frame’ of the natural numbers. Nothing happened to them.

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Yet there was a bigger surprise because a new pattern was noticeable.

Since I followed my own path to discover what was going on with the prime numbers, I stumbled upon the fact that the larger amount of patterns were discernible when all natural numbers are placed in lines of six.

Other rows of numbers were also promising, pattern-wise (for instance, with rows of 5 numbers, and rows of 30 numbers). But the best view occurred when the natural numbers were stacked in six-packs. Of course, this information is nothing new to the initiated. Everything thus far had already been known, with Eratosthenes the first to write this all down.

The opening phase of the bigger surprise was that the non-prime numbers pointed me to an additional pattern that linked all numbers found in first and fifth positions in these six packs.

Knowing this newly discovered pattern, all non-prime numbers can be appointed, ad nauseum, shown further below.

The bigger surprise itself was that this appointing pattern contains a spot in which zero must be used.

Up to that moment, I understood that zero was not seen as a natural number. I knew from that moment on that zero is a natural number. One cannot work with natural numbers only, then stumble upon a required use of zero, and still declare that zero is not part of the whole group. That is not how science works.

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Does it matter that zero is a natural number?

In an example, many scientists declare that there is no Year Zero. Our calendar starts out with the Year One CE (Common Era), and the prior year is the Year One BCE (Before CE). Nothing exists in between.

Too bad for these scientists that the number of years between January 1, 500 BCE and January 1, 500 CE adds up to only 999 years. A year has gone missing, and that is not handy. This confirms that zero is indeed an essential part of our calendar. Zero matters.

Adding a functional zero to other systems can have far reaching consequences, for instance, how we view the Big Bang process and Black Holes.

• Twin sibling of the Big Bang theory, the Big Whisper theory is centered around this mathematical information and declares how separation is the first and most important universal action in light of matter. The materialization process started up among original energy with establishing an empty position within. Only parts of the prior energized state ended up becoming matter — not the whole of all original energy. A fundamental change had taken place and is best expressed with 0 found among the entire set of energy.
• Black Holes can end up being seen as Black Eyes when not matter but a fundamental empty position is found in the center. Instead of a mass explaining the gravitational monster, the collective of all masses in a galaxy establishes a gravitational depression in the center. That depression is a synergistic outcome best expressed with 0 found among the entire set of gravity.

Incorporating a fundamental zero changes the setup of our thinking.

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Here is the pattern information.

There are five steps to follow in total to make the pattern(s) obvious and to point out where zero is required. This is mathematical evidence, though it needs to be understood that this is evidence about the foundation of math, about the mathematical building blocks.

Take a look at Table 1 as the introduction. In this table, the numbers between 1 and 100 are placed in lines of six numbers. In these “six-packs” (7–8–9–10–11–12 or 19–20–21–22–23–24) prime numbers will only be located in first and fifth position (7 and 11, and 19 and 23). They are shown in green and there are two exceptions: numbers 2 and 3.

To keep it simple (because we’ll be moving away from the prime numbers in Table 2), number 1 was also made green, though this is officially not seen as a prime number. Note that it, too, is a number with not much happening to it.

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Step Two: In Table 2, the highlighted red numbers are numbers in first and fifth places that are themselves not prime numbers. It turns out that these red numbers are all various multiplications of prime numbers. Follow the color code in the table and it becomes apparent that all red numbers are multiplications of green numbers with the exception of 2 and 3. For example, 25, 35, 55, 65, 85, and 95 are numbers in first or fifth positions divisible by 5.

[To be accurate: the multiplications are not just based on the green numbers, but on all numbers in first and fifth position. In Table 2, all red numbers are indeed multiplications of green numbers, but had the table continued then the red numbers would become visible, too, as used for these multiplications. For instance, 5 (in green) x 25 (in red) would point out that 125 is not a prime number.]

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Step Three: In Table 3, the specific outcome for 5 is made visible. The square of 5 is found in a line of six numbers in first position. Next, 35, is found one line below in a fifth position in a line of six. Next, 55, is four lines below in a first position. There is a pattern, and it is shown in this Zigzag Figure. The pattern for number 5 jumps 1 + 4 lines, while zigzagging toward the larger numbers forever.

In Table 4, the zigzag pattern for prime number 7 is shown. The pattern jumps 4 + 3 lines forever.

In Table 5, the zigzag pattern for prime number 11 is shown. The pattern jumps down 3 + 8 lines forever.

In Table 6, the zigzag pattern for prime number 13 is shown. The pattern jumps down 8 + 5 lines forever.

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Step Four: All these patterns have a pattern among them, called the Link Pattern. As you can see in the image, the pattern is predictable. The 4 found with the pattern of number 5 reappears up front with the pattern of number 7. The second part of the pattern with 7, which is 3, reappears upfront with the pattern of number 11.

As declared here just with number 11 and then for number 13 as examples: when the first part of the pattern for 11 is 3, then the second part of the pattern is 8 (11 minus 3). This 8 is then the first part of the pattern for number 13, and so the second part is also known (13 minus 8).

And on and on it goes, everything pattern-wise is known, all the way to foreverwith these first-and-fifth-place numbers (whether prime number or not).

All prime numbers can be known using this Link Pattern. The Link Pattern does not make any calculations; non-prime numbers are eliminated based on their positions. What remains are the prime numbers in first-and-fifth positions.

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Step Five: The last step to finding the required use of zero occurs with walking this Link Pattern back to number 1, as shown in the table with Step Four.

The specific pattern combination for number one is 0 + 1.

The jump pattern is an actual stop on the same line and then a jump of one line. You can see it in Table 7.

Notice how, in this table, number 0 was added to the list, so first and fifth places for prime numbers and the likes are now in second and sixth places. Nothing already shown changed fundamentally, but positions were changed by adding a fundamental zero.

While there are other setups available to view prime numbers (5 numbers in a row, and 30 numbers in a row), they do not have the neat explanations as found with 6 numbers in each row, nor do they show the necessary use of zero because the underlying principle is less clear.

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These are the five steps. The evidence that zero is linked to the other numbers lies in the fact that its use is required to name the specific pattern of number 1. Without zero that pattern cannot be named or explained.

This is the evidence that zero is a fundamental part of what may initially appear quirky and unimportant, but what is nevertheless an essential part of this rather basic pattern found in math. Notice that the important part is not what zero portrays in reality, but that its use is required in this pattern.

This is the essence of the entire article:

There is a function associated with zero that no other number can portray and that is natural nevertheless. Among all functions in the universe, we find the function of separation to be fundamental, universal.

In plain English: When zero is unimportant, then the universe can be seen as a ‘marriage’. Yet when zero is (at times) important, then the universe must be seen as a ‘divorce’.

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There are two groups of mathematicians: set theorists and number theorists.

Number theorists do not have a Year Zero. Set theorists do have a Year Zero, mainly because it is unhandy to add and subtract that one year all the time when talking about information that spans thousands of years, for instance in astronomy. For them, 10,000 years ago is exactly that, and not 9,999 or 10,001 years ago.

Both mathematical groups don’t worry too much about this fact and at times many mathematicians declare to start out with the empty set. Now there is evidence that zero is a number always found among the positive integers.

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Let’s investigate the largest of levels further.

Finding zero as a natural number, we must replace the natural number sequence starting with number 1 with the real natural number sequence starting with number zero.

Therefore, there are two distinct number sequences.

It is important to not discard the artificial number sequence. Like a painting, or like money, artificial realities can be extremely beautiful or even vital up to the highest level in our lives. It is very common for people to make use of number 1 as the highest position for our most important structures and institutions. Artificial realities can take in prominent positions as long as we united (1) ourselves around them.

It gets a bit tricky to place zero in top position, though God seems to fit that spot rather nicely.

When looking at the universe, money is a non-issue. We are the ones subjected to a financial reality — it makes us climb out of bed every morning — yet the sun rises without any knowledge about money. An impressive painting on the wall does not move the moon in our skies. A meteor has no respect for Trump, Xi or Putin, or the head of the United Nations for that matter. For us, the artificial realities we united ourselves around are important. For us, this single 1 is mighty important. But for everything else in the universe, 1 is just one of the numbers.

Our universe came into being because zero plays a central role. In the middle of everything, we find zero.

Climbing a mountain, for instance, is done with steps first going up. When at the top, we experience a wonderful view while taking steps to walk around at that ‘flat’ level. Next, we walk down the mountain again. The pluses of going up and the minuses of walking down have zeros right smack in the middle where we were taking in the view. In this perspective, one can find zero at the top of the mountain (and we can experience being 1 with it all).

Zero is non-singular. Number 1 can be singular, but zero is not. Like walking around at the top of the mountain we can use zero to describe the action of not climbing and not descending. Yet when we walked back down and got to basic grounds, we can also use that same zero to describe our action at that bottom level. Both zeros, identical as they are in our minds, are not identical, an entire mountain found in between. Zero is non-singular because it describes both a correct action from ground level and a correct action from the top.

Much simpler is showing that 0 is not one and the same by pointing at 010. The first zero is not the same as the second zero. The second zero is required, because without it the number changes dramatically. The first zero is, however, optional. We can place it there or not, and it does not affect the total of the number at all.

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The material universe presents us two actions.

With matter, one can see a divergent and a convergent action. The divergent action occurs at the collective level with an outwardly moving (divergent) action among all matter, away from the Big Bang/Big Whisper beginning.

The convergent action, of matter hanging out together, occurs at the ‘local’ level. Galaxies are the largest areas for matter to congregate (showing a level of convergence).

With the Big Bang/Big Whisper process, we must use number zero to express the essential action of separation we see occurring in our material universe. This divergent action happened once and it is not repeated, though this can still be discerned in the material facts of our universe. Matter does not exist with this zero. Matter exists in the aftermath, after the original separation occurred.

The divergent action and the convergent action seen among all matter are not linked. If we use numbers for both situations, then 1s and 0s are used in specific spots in each perspective, each with swapped positions. Where we find convergence (1), we find no divergence (0); where we find no convergence (0), we find divergence (1).

The binary system appears to express best what the universal system is.

The idea that singularities can exist must be rejected. Note how the idea of singularity is not an automatic aspect in the binary system. It can be conjured in the binary system, but is not a natural part. The decimal system also does not contain singularities, but in that system the human mind can put 1 in first position (where in reality 0 is found) and then claim that singularities exist. We can fool ourselves that way.

With the evidence that zero is a natural number, the idea that all can be brought back to a single level cannot be correct. Even when convergent behavior of matter is ubiquitous in the universe, at the universal level itself there will always be a secondary aspect, undermining that ubiquitous behavior.

Not having an ultimate unification is a central feature in the Big Whisper theory that proposes a ToE of two levels (one level being the synergistic outcome of the components on the other level). Said differently, unification can get found at the specific level, yet the lack of unification is found one level up, with the overall reality of our universe.

Gödel already showed us the Structure of Everything with his Incompleteness Theorems. His work is still not recognized fully for what it shows.

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Looking for the missing pattern among prime numbers, we can see how the material universe is organized. By including a fundamental zero, the setup we use to explain Black Holes and the Big Bang can be altered since they cannot contain singularities.

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Delivery based on The Proof of Nothing — a theory of everything, published by Penta Publishing (2000) and In Search of a Cyclops (2003), internet publication.