Goldbachs Conjecture Proof: My Almost-Final Answer

Let us see if it is possible to violate Goldbach's Conjecture. Suppose we take two lines of even, whole numbers, counting in opposite directions, and line them up one on top of the other. If they are 126 long, 0 in one line will be 126 in the other.


6 5 4 3 2 1 0

0 1 2 3 4 5 6


Now suppose we insert a wave of every prime frequency, including 1, into both. At 1 in each, we will get 1, and 1 again at each number through 126. At 2, we will have 2 and 1 - for a total of 2 - at 3 we will have 3 and 1, and so on. At 15, we have 5, 3, and 1, for a total of 3.


0 1 2 2... 3

0 1 2 3... 15


If we load both these number lines with all these frequencies in this manner, both lines will contain the same amount of data in their linear variations, meaning the same amount of entropy or complexity. Complexity is the same, whether you're talking positive or negative space.


But, suppose we flatten these lines, so that they are at either 1 or 0, never 3, like 15. If 15 would be 1, we don't need 3 and 5, just 1's! But suppose we throw away 1's, bar them from our use, and just use waves of prime numbers 2 and higher to fill both from the opposite directions.


The entropy of these lines should be the same, or perfectly opposite, whether you look at their prime holes - meaning 3,7,17 - or their prime frequencies - meaning 121,123,125. They are the same data, no matter how you look at it.


Except for one problem. Each line has a hole in the form of an original 1, which cannot be used as a frequency. And by putting the 1's at opposite ends, it is just impossible to line them up opposite each other! As such, it is impossible to have a hole in 1 line for every frequency in the other.


In other words, each line is theoretically just complex enough, in terms of its time-series variation, to exactly cancel out the other, except each line has an 1 extra hole without a corresponding frequency.


Any time there is a hole left where a prime in the top line sits opposite a prime in the bottom line, that means you have two primes, counting to each of their zero's, which must add up to equal the positive, even sum which is the length of the number line.


Once we elimnate 1's, and the possibility of staggering opposite two-waves by an opposite number, our reduced-entropy linear compaction must marshall the full entropy of both lines to offset. Of course, if we were to allow the vertical stacking variations, the problem would only get worse.


If we used only 3-waves, we could achieve complete smoothness with three staggered lines. But in this challenge, we need to use two lines, so as to measure two primes from one spot to two zeros in two different directions. But the compacted resolution smoothness which could be masked over using staggered two cycles is eliminated using even numbers. And with only two number lines, all remaining frequencies would theoretically be needed to achieve smoothness.


Any number of cycles where, say, the first 10 primes would synch up again - like they were at zero - would invariably take a longer number line than one limited to those primes. Any number line will always contain a sufficiently large prime number that would take a longer number of cylces than the number line itself to fall back in synch with the other primes it is lined up with at zero, and become useful as a frequency.


Another way of saying this is that the complexity is asymmetric, and trapped at opposite ends. Before all the lower prime waves at the wave end will ever fall out of synch enough to disaggregate their complexity, and fill every prime hole at the prime end, an endless stream of new, complex prime holes from the other end will emerge in the middle, to be filled. Every prime is a hole, long before it becomes useful as a frequency.


Notice, I am not saying you need an equal number of holes and frequencies. I am simply saying you need an equal number of out-of-phase frequencies to describe where the holes are. Incredibly, if you use up an extra hole at one end, by using it to describe a hole instead of a frequency - and it does not sit opposite itself in the middle - you end up having two hanging frequencies describing a frequencies, and two more holes which must be used to describe on another.


And, you still always have those two hanging holes at both ends. If you cover them with a frequency, that means there must be at least two hanging holes somewhere in the middle, sitting opposite one another. And that, in addition to the problem that in-phase waves in the middle - where new holes are being created counting from the end - are already creating missing frequencies and extra holes which must sit opposite one another.


So, in summary, an AND hole which is prime to both zeros on an even number line fulfills Goldbach's conjecture. And the naked 1's at both ends guarantee there must at least one such hole somewhere in the middle, since we cannot manufacture an extra frequency without the use of 1's, even with vertical compaction. And the further asymmetries on top of that, guarantee further holes in any number greater than 2.


eLROY

Let us consider the even numbers 18, 20, and 22.


22 has an odd number of holes, because 11 and 11 sit opposite in the middle, and all others pair off. 18 has a frequency in the middle, which seems like it should create two hanging holes - which could sit opposite the original or 1-implicit holes - so it would have an even number.


As such, it makes sense 22 would have 1 fewer holes than 20 - which also includes 19 on its line - but more than 18 - which doesn't have 19. 18 can't single-hole the 11, but it has a hanging frequency in the middle, which balances out its not having 19's when its 17's sit opposite its 1's. Meaning, the 17's are so far apart, and they can't sit with threes, they have to creat a hanging frequency in the middle.


22 has a lot of primes that are not yet fully used as a frequency, 5, 7, 11, 13,17, 19 - if you consider each prime to be "under-utilized" until it reaches its square. And 22 has 2 holes one each side - for a total of 4 apart from its 1-implicit, for a total of the 6 asymmetric and under-utilized frequencies in both directions - which doesn't add up when we take care of 17 - which just really means we have hanging frequencies at like 2 and 20, it all balances out.


Notice, 18 has these same under-utilized frequencies except 19, plus the split 1-implicits, and the hanging 3-wave square frequency in the middle. After each prime's square, the next time it really becomes utilized is as a frequency paired with the next higher prime that has not reached its square. So 3 becomes useful at 9, and then at 15, but is a hole at 3, and covered by 2's at 6.


Any smarties want to correct my work so far?


eLROY

Speaking just for myself, I'm finding your posts very difficult to understand. The one I felt closest to understanding your argument was the one posted at 5:57 A.M. from which the following is an excerpt:


"Therefore, using these axioms, the proof is simply a proof that there will be a prime number higher than any given prime number, but lower than its square, or you get the idea. For an illustration, consider the positive, even numbr 126, which makes separate use of 11,7,5,3, and 2 at its terminus. We already have the prime wave 13 available to describe this region, and we're not even talking half way to the midpoint!"


I suggest you break your argument into pieces, similar to the following:

Axiom 1: Blah

Axiom 2: Blah, blah

......

Axiom n: Blah, blah, blah


Proof (State conjecture)

Given Axioms 1 and 2, it follows that ... and so on.


That is, state exactly what it is you're trying to prove, what your axioms are, and how, given the axioms, the proof would follow. Then we can look at the reasonableness of the axioms and the logic assuming the axioms are true.

tewall,


For a quick up-to-speed, check out my first try in the Stocks forum. You will see my plain error if you start counting down in 3's from 32. They fill both the 29 hole and the 3 hole in the opposite direction, among other things. But it is illustrative of my initial path of thinking, starting at nothing. So, here's my first try:


AXIOM 1: A number line is a linear variation expressing a certain amount of entropy. Look up Huffman coding on the web. It is a sequential collection, to the extent it is unique not just in the number of 1's, 2's, 3's and zeros, but also because of their order.


AXIOM 2: If you take a single wave, its entropy is implicit in its frequency and amplitude.


AXIOM 3: You can populate a number line with linear variations, by starting at zero, and then laying down a 1 at every slot where a prime wave - 5 - or its frequency - 10, 15, 25 - touches down. And you don't need 4's, only 2's. At this point, the entropy of your number line should be the total entropy of all the waves combined. In other words the entropy can really be expressed in terms of each prime hole and its magnitude.


AXIOM 4: When you flatten each slot, to instead of registering the total magnitude of waves hitting it, to only register a binary of whether it has been hit by a frequency or not, you lose - or make - some entropy at "frequencies," so that the new entropy is a complex product of every unique wave interacting. Meaning, the product is now unique based on not just the included waves, but their order, order becomes relevant


AXIOM 5: When you synchronize prime waves to begin at zero - meaning two are not on the same spot on the same number line, and none are a frequency starting at the zero of another, that is a unique entropic collection.


AXIOM 6. The frequencies laid down on the 1-dimensional line should have some complexity which is related to the primes you have included, and their order - meaning their synchronization around one. But where frequencies coincide, but are suppressed, the product must be a simpler strecth of line than if they were not. And since entropy is a concave function of distance in relationshio to conplex objects, in ordered adjacencies, a section which is closer to the suppressed region and further from the out-of-synch region must have less complexity, from its point fo view.


AXIOM 7: To construct the Goldbachs example, we had to deade the vertical component, because all we are trying to do is fill holes on one line with frequencies on the other. But since we are suppressing addition, we have to suppress the 1 frequency, which woudl run rampant across the number line and mask all variation. Two's would do the same thing if we staggered out lien by odd numbers, but fortunately we are dealing with even numbers. Also, Goldbach's Conjecture specifies a sum of two primes, we can forget about zeroes at both ends. But, we have to keep the 1 primes.


AXIOM 8: The total entropy of each line - the suppressed entropy product of the primes included - must be identical. Furthermore, they must be equally complex if inverted, since complexity does not distinguish as to between positive and negative space. Meaning, if you switch every 1 for an 0 and every 0 for a 1, the entropy remains unchanged.


AXIOM 9: The entropy in each separate line therefore remains equal if we switch holes and frequencies, so that, collectively - meaning not in any particular adjacent order - they could cancel one another out, or describe one another. Frequencies in one could be used to describe holes in the other, except two problems: 1, they are laid end to end in opposite directions, and 2) they both have a 1-hole whose frequency is suppressed - meaning frequencies are not a complete product of holes and their order.


AXIOM 10: Therefore, a hole must be opposite a hole somewhere, both because there are 2 extras to match off, and because, suppressed to binary coincision, and at a distance, frequencies are not able to perfectly describe holes. You must subtract an eqaul number of frequencies and holes from both lines, to arrive at a descriptive combination. The way you subtract frequencies and holes on oppiste sides, without using them to describe each other, is by placing them opposite each other in the order. To resolve the asymmetries, there must be at least one hole.


Mind you, this is not my last word. I have to go back through what I have written and brainstormed, and see if I didn't miss or misinterpret a critical axiom somewhere. In any case, and in additionb to any corrections, I would like to add more proof, and more imtermediate axioms, anywhere I can. And I will do so in subsequent posts.


Did I miss something?


I assume I did. I'll go back over everything I've written, and add more.


Thanks for... caring


eLROY

Yes, like the definition of an Axiom in your first high school math class.


I don't think you have had any formal mathematics training, and if you want to prove Goldbach's conjecture, it might be a good idea to get some. If you have had some, then you've forgotten a lot of it.


You're wasting your time and ours with this nonsense, but especially yours.


And don't even ask me to try to explain what you did wrong. You have so many of your own definitions and techniques that haven't been properly outlined that it is impossible to figure out what you're talking about. Your writings seem eerily similar to those of schizophrenics, and you seriously might want to talk to a shrink.

Yes, when a unique entity is so complex that no simplification or generalization can be used to describe it or apply rules to it, it remains intractable to a less complex entity.


eLROY


P.S. Why ever would I go pay to sniff chalk dust with a bunch of patch-pants boobs, who have failed utterly to prove this conjecture for the last 250 years, despite every miserable effort?


Your half-brained mathematical "methods" can only be used to prove the exact location of the first hole in any particular series, and only by using a description of that entire series as an input.


Your tools are incapable of uncovering a single common property between any two series of prime waves. And no, I didn't take math in high school, and I had to look up "axiom" in a dictionary just now.


How am I supposed to know what particular axiom some college-trained idiot won't understand? Obviously, I can predict that if any Goldbach's proof is discovered, the axioms used will be alien to the mind of the common limp-wit, or he would have simply assembled them and solved the problem himself long ago.


Of course you don't buy my argument, you moron. But what you don't realize is that you would have the exact same reaction no matter if the correct argument stared you in the face.


Both the correct argument, and an infinite stream of flawed ones would be indistinguishable to you. But you know, good luck, the world needs idiots too.

You wrote:

How am I supposed to know what particular axiom some college-trained idiot won't understand? Obviously, I can predict that if any Goldbach's proof is discovered, the axioms used will be alien to the mind of the common limp-wit, or he would have simply assembled them and solved the problem himself long ago


No, the axioms WON'T be alien to the mind of the common limp-wit. That's the point of an Axiom: its an easily understood statement. Assembling proper axioms in order to reach proof is the difficult part. Understanding the axioms is the easy part. If you've found a new method of proof beyond constructing a logical argument that builds upon basic principles, I'm excited to hear it. That would be more important than proving GC.


Good luck, eLROY, seriously. I read the New York Times so I'll be sure to see the article about you when you finally prove GC.

Each prime wave - 7,13,17 - occurs at its own spot one time. Therefore, a map of 0 through 3, with a binary resolution, will reflect completely the entropy in these waves.


You dead the slots, so that 15 doesn't reflect 3 and 5, but rather only that at least 1 of them was there, you lose some data.


To prove Goldbachs's conjecture, all I need to do is prove that I can't fill - or "describe" - the full-resolution prime holes with suppressed-resolution product frequencies.


And all I need to do to prove that is prove that the product frequencies are less complex than the holes, since, if you take the number 34, it has an 11 hole, but the frequency 11's are buried inside 22's and 33's.


The fact that I also have a 1-hole to describe, but I can't use a 1-wave - or else it would completely pin an entire binary-resolution number line - is just icing.


Or, the fact that, like gravity, complexity is a function of proximity (every code is a subset of a larger code) - so when the lines are overlayed in opposite directions you must have a net complexity gain or loss, not a cancel-out - seems pretty obvious to me.


Is there something strange about the idea that the entropy of a wave is the function of its frequency, such that the higher the frequency, the higher the compelixity?


If we can smooth a number line with three staggered 3-waves, and it only takes two 2-waves, and therefore 2 must be more complex or precise - when it is positioned in proximity or relative to 3 - am I going out of bounds?


eLROY

Don't get mad, but I agree with EssW regarding axioms. However, we can leave that part aside, as an argument can be made rigorous later assuming it's valid.


Basically I'm understanding your argument is:

A) You have a conjectuture which is equivalent to Goldbach's.

B) You have a way of proving your conjecture.


A couple of questions.

1) What is your conjecture?

2) Why is your conjecture equivalent to Goldbach's?

Okay, here's 2 and 3 waves, harmonizing on a binary number line:


. . . . . . . . . . . .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16


As you can see, they go 3-space-1-space-3-space-1-space. How complicated is that? Moreover, you could bury an 11 in one of these, and, other than at 11, it wouldn't show its face again until 121!


But now lets look at primes, marked out on the same line:


. . . . . . . .

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16


The primes go bang-bang-bang-bang-space-bang-space-bang-space-space-space-bang-space-bang-space... and I'm still not done!


And I never will be.


The primes are the antithesis of frequencies, they literally - by defintion - defy as many waves as possible, no matter how in or out of phase. The primes have no darn harmony whatsoever.


They are literal disharmony sniffers, guaranteed non-cycle detectors, if you don't have every necessary penny of entropy available to you - every penny up to as much as they, themselves describe - they will by law stumble upon at least one way to evade you.


By the laws of physics, one must escape!


Is this not axiomatic?


If this is not axiomatic, I don't know what is. Are we living in 5,000 BC?


eLROY