You know, I majored in math in college, and yet sometimes I have problems following other people’s mathematical trains of thought.
Please bear with me, because I’m intrigued.
You’re separating all even positive integers, greater than 3, into whether they fit into certain groups. For some groups (or for all groups?), you can predict things about the primes that will be found to add to them.
114: The difference between 61 and 53 is 8, and 8 is of the form 6(2n-1)+2. Just like you predicted.
And you have other predictions about the *differences *between the 2 primes for other classes of even positive integers. And if somebody could use those predictions about the differences between the primes in some yet-unseen way, they might be able to prove (or maybe disprove) Goldbach.
Have I got that right?
Maybe you want to actually work in base 12 or base 6. It might make some of the mucky-muck fall away.
I don’t think the assumption **armstrongm **hasn’t taken number theory courses is warranted.
I think that we all agree that Goldbach’s conjecture is true. I certainly do. But I don’t know. Now I will be honest I have taken 0 number theory courses everything I know about the subject is self taught but I appreciate the defence.
I have created 6 classes of positive integers using base 12. I use that as a base because 6n+6n =12n.
Let us take 6 different positive integers. For this example I am ignoring three I am well aware that three and a prime will result in certain positive integers but I can not predict the qualities that this positive integer will have. I can make predictions using three in the future but for the time being I will ignore it. I can also give a guarantee that the maths is 100% sound and I have a proof. I just ask that people look at the idea and see if it is new and would be considered for publishing. When I say they I mean the two primes that add together to result in the even number that I am defining,
Numbers that can be written in the form 12n. They must be the sum of two primes that have a difference that can be expressed as either 6(2n-1)-4 or 12n-2.
Numbers that can be written the form 12n+6. They must have a difference that can be expressed as either 6(2n-1)-2 or 6(2n-1)+2.
I know that those are two groups and they are easy to comprehend. For the next four however, things start to get weird and confusing in a hurry even if you are looking at the maths.
Numbers that can be written in the form 12n+8. They must have a difference that can be expressed as 6(2n+1)
Numbers that can be written in the form 12n+4. They must have a difference that can be expressed as 6(2n+1).
Numbers that can be written in the form 12n+2. They must have a difference that can be expressed as 6(2n).
Numbers that can be written in the form 12n+10. They must have a difference that can also be expressed as 6(2n).
That covers what the maths is telling me. I couldn’t make this up even if I really thought about it I’m not that clever. These are truths.
Now if one were to prove that these equations could work solely with prime numbers then they would have proved Goldbach’s conjecture. That is what I am saying. That this the prediction and possibly what it may lead to in the future.
I think you have missed everything that I have been saying. I mean that with all respect in the world and it was probably my terrible explanations earlier rather than you.
In an earlier reply I went into more detail. The partitioning is simple its beautiful in many ways for that reason. That is not its problem it has limitations but not for the fact that it is simple. I am not silly I know that this is minor it wont shake the world. I know its limitations and I have been careful to only state the facts.
What this is saying is simple. If an even number can be the sum of two primes greater than three. Then these two primes must have a difference that can fulfil a certain expression. This expression is dependent on whether the even number can be expressed as: 12n; 12n+2; 12n+4; 12n+6; 12n+8 or 12n+10. That is a truth and I would be happy to send you the proof. That is all that it is saying in reality. I did speculate what the theorem may lead to and I am sorry if that caused confusion.
I think a big problem has been that you don’t have the vocabulary needed to properly express your ideas, and also don’t have the experience to appreciate the amount of pedantic precision needed in order to avoid misunderstandings and misinterpretation of what you are trying to say. Things like talking about equations when there are none really makes it hard. It becomes a matter of second guessing the meaning behind your words, and that is always going to end badly.
Please read up I have mentioned many equations and described their predictions. There are 10 pages of just equations that I have and to write them all down here will take me 6 hours and I don’t have that time. So please read my previous posts the more recent ones go into great detail about what each equation predicts. If after that you don’t follow what I am saying then feel free to ask and I will clear up the misunderstanding as best as I can.
In all seriousness, I don’t have the time to do that. (I do understand what you are saying, that wasn’t my point)
You are saying that you don’t have the time to express your ideas in a coherent manner, but you do expect that everyone else has the time to decipher your ideas. And then you expect them to critique them, and engage in discussion about your ideas, for your benefit.
My point was that you have been battling against your lack of expressive ability and experience in attempting to engage in discourse. You asked earlier about pointers to expand you capabilities that didn’t involve taking a formal course - this link was provided in that spirit.
This forum has many professional mathematicians, and a lot more that have taken university level mathematics - including number theory. If you want to engage in useful discussion, and enjoy the idea of playing about with the mathematics, it would help everyone if you did do a little spadework. Otherwise you will probably exhaust everyone’s patience - and really that isn’t an outcome anyone wants.
Which equations or explanation is unclear that is all I ask. I am not trying to be difficult I really appreciate the help. If you tell me what is unclear I will explain it 1000 times if that is what it takes.
> I think that we all agree that Goldbach’s conjecture is true.
No, we don’t. It’s suspected that it’s true, but it hasn’t been proved. We’ll all agree on this when it’s actually proved and not before.
You wrote mathematical expressions like the following:
12n
12n + 2
12n + 4
12n + 6
12n + 8
12n + 10
You keep referring to them as equations. These are not equations. They are mathematical expressions. To be equations, they would have to have equal signs in them.
Frances Vaughn has given you a link to a book that’s available completely online for free. Read it, and come back to us when you have questions about it. At the moment you don’t have enough familiarity with how mathematics works to even begin discussing a proof of Goldbach’s conjecture.
You have misunderstood what I am saying. I cannot prove Golbach’s conjecture you are right. There are so many challenges to prove it that I would not even know where to begin. I am sorry for call them equations I will call them expressions from now on.
Now whether Goldbach is correct or not is irrelevant. I am certain it is true for two reasons. The first reason being the number of potential primes that can be added together to create an even increases as one tends to infinity. This in my mind means that the chances of it being true increases. The second reason is that it has been tested to such high values and found to be true that if were proved false I would be very surprised. But it may be.
This isn’t a proof for that conjecture. I can’t do that I’m not good. You are right I don’t know a lot of mathematics. But the maths I do know I know very well even if that is limited. So I will tell you what those expressions are telling you. In my reply to bup I mentioned what each of the expressions and what they are showing.
In essence what they are saying is this. The difference between two primes determines the properties of the even number that they create when added together. Such as if the even number can be expressed as 12n; 12n+2; 12n+4; 12n+6; 12n+8 or 12n+10. In my reply to bup I listed the expressions for these differences. I have proven this. I am not asking whether this is true or false. I have proven this mathematically.
the question was whether anyone has re-defined Goldbach’s conjecture in this way before and whether it is useful.
In what way to do you battle with the constraints?
12 = 5+7
24 = 11+13
14 this value is too low to satisfy the constraint. If you think about it 14-12 =2. Two is too low to satisfy the condition of 6n+1 or 6n-1. Now before people roll their eyes think about it. I have this with differences and have excluded the prime of 3. If I were to include it. 6n-1+3 = 6n+2. That would satisfy 14. But I admit the equations I have fail to satisfy 14. The rest though are fully satisfied for n=1 and n=2
Clearly I’m misunderstanding your constraints. Don’t you also have subtraction constraints? Here’s the way I understand your conjecture about the “difference between primes” and how it relates to each of these numbers:
For all n >= 1, there exist 6 pairs of primes, [(p11, p12)…(p61,p62)] such that
Meaning: For all numbers n there must be a pair of primes that adds to some number (e.g. 12n) and also have an absolute difference meeting some constraint (e.g. 6(2n-1)-4 or 12n-2)
Of special note, all pairs must be distinct. That is, (p51,p52) must be different from (p61,p62) – for all n; 6(2n) has at least two separate prime differences that produce the same value.
Why is that? Because, by your conjecture:
p51 + p52 = 12n + 2
p61 + p62 = 12n + 10
Obviously these can’t be the same pair of primes unless they made a change to addition I wasn’t informed of.
The problem is, I can’t satisfy this when n=1 or n=2. Haven’t tried anything higher.
The difference between primes can be between any two primes greater than 3. So the difference between 5 and 19. 7 and 19. So not Prime1 and Prime2 but Prime(n) and Prime(n+a).
Constraints for differences? Not really I have equations that define the difference between any two primes though. This so if you have two primes n and n+a.
If n can be defined as 6n-1 then the difference between these two primes is limited there are certain values that it cannot be.
Those difference equations will work for all differences of n. That there isn’t a doubt. I don’t add the differences to create the expressions
12n
12n+2
12n+4
12n+6
12n+8
12n+10
I use the expressions for the two prime values and ass those two together. I don’t understand your equations and can’t follow them. I’m sorry for that.
If we now say that the primes can have a ‘limited’ number of differences in that there are certain differences that cannot exist between two primes then it that sense there are constraints.
This doesn’t affect the expressions that I use to define the evens. It just is so that you can see where it comes from. If you give me your e-mail address I will e-mail you the full proof if I can’t answer your question.
12n+10 comes from two primed having the difference of 12a. X is a natural number it need not be the same as n. So in 6(n +2x) +1 2x denotes the difference between the two primes.
> You are right I don’t know a lot of mathematics. But the maths I do know I know
> very well even if that is limited.
No, you don’t. You may think you know some mathematics well, but you don’t. Read that book that Frances Vaughn linked to. Or take some courses. There must be some nearby place where you can take courses cheaply. I’m not even convinced that you understand high school math well, let alone college math. Find some place that offers remedial math courses. Until you understand them well, we can’t help you.
You would know hay because you’ve seen my maths tests. I don’t appreciate such comments. I’m not rude or insulting to you so why would you be to me? It’s not fair or constructive criticism. The maths is 100% correct If you would like I will e-mail you the proof.
I’m not asking you to critique my maths. I don’t care for your opinion on the actual maths. The suggestion that I take remedial math is silly. I’m not going to sink to your level but I will say this. The maths I know the mats I did at school, going to university in February and done with my A-levels, the calculus and algebra I know 100%.
You don’t know what I know. So don’t comment on that it is an uninformed statement.
If any of you think the maths is wrong then feel free to tell me where and I will show why it is right and explain any misunderstandings. I can do this algebra in my sleep it isn’t hard. I know what I know if that makes sense. If I think you have brought up something that I missed I will be the first to admit it. I am not full of pride I know where my abilities end.
This maths, the very same you say I don’t understand, I got 100% for 5 years ago. Think about it I use it every time I do maths. It’s like telling you that you can’t ride a bike. It silly. You, I think, have not bothered to read my explanations on anything. Calm down and come back when you’ve reconsidered your position.