That is a misunderstanding. Let me clarify it properly now that I have found the document where I got it from.
Let me take this expression by expression.
12n.
When I say that this can be achieved by adding to primes with the difference 6(2x-1)-4 and 12x-2.
I
n this instance when I say x is one I get 2 and 10 for each of the expressions.
If I were to create to lists of prime differences: 2; 14; 26 etc. For the first expression the value of the x corresponds to the term number in the above sequence.
Now if I were to list the primes: 10; 22; 34 etc. for the second expression the value of the x corresponds to the term number of this sequence. When primes with either 6(2x-1)-4 or 12x-2 are added the end result is 12n. The x and the n do not correspond.
I hope that clears it up for all the other expressions as well.
Really, I do think it would behoove you to take a course, or at least work your way through a good book, on Number Theory and possibly also on mathematical proof. If you’ve taken algebra and calculus, you may not have had much exposure to mathematical reasoning and proof techniques of the kind you’re wrestling with here, nor had to write out any mathematical arguments and have them critiqued by a mathematician, nor gotten a feel for the kind of language and structure that mathematicians use when presenting mathematical arguments. I.e. I agree with what Great Antibob said above.
I’ve studied proof techniques, brute force which is basically what I did here, proof by contradiction and induction. I’ve written many proofs and had them checked in order to make them clear I know how to express my mathematical ideas properly thank you.
This is simply algebra and then explaining the algebra in words its not hard. You simply have a limited mind in the sense you are unable to look at it with an open mind. You think, wrongly, that any idea that I have must have been thought of already because let’s be honest he hasn’t done university so he must be wrong. So limited imagination and reasoning capacity.
It is easy to just say, “I don’t understand it must be him!” Even if you are right you don’t bother asking what I am saying or an explanation. Sure my explaining my be hopeless. I accept that it has never been a strong point of mine. So why not tell me you have been unclear here and there and have me explain what I mean?
No you don’t bother. My ability to reason and critique my own maths is much harsher than what you have done. I can spot so many limitations they are everywhere. That is why I am general when I speak about it I’m never specific. Not to try and confuse but because the maths does not allow me to be. It’s not that clever.
The proof technique I am wrestling with here is rather basic and crude. For that I apologise I did a complex one but that was 50 pages not 12. The maths here is effectively equating two sides of an equation. Proving the left and right hand side are equal. Its not complicated. I don’t need to use complex proofs and techniques for what I have done. It’s not that clever.
In the instances where 6x+/-1 is not prime but composite, there appears to be a regular distribution…in this admittedly small sample of primes under 100.
Where 6x-1=(6x-1)(6x+1) we find examples of composites, not in (6x-1)^2 or (6x+1)^2.
Also, there appears to be no examples in 6x+1=(6x-1)(6x+1) and very few (one example) in 6x+1=(6x+1)^2.
Does this apparent distribution hold true indefinitely?
Does this figure into Goldbach?
I really want to say yes more than anything. I do have a few concerns that aren’t fully adressed. On the assumption that this is true it would not be sufficient. For at least one reason I can see. If you are asking me if this with what I said would prove it I would lean to no.
I don’t think it is because my conjecture will still include them and therefore invalidate the proof.
Whether he knows math(s) or not well enough to satisfy you, he is making observations about the prime numbers that will be found to satisfy 6 subsets that make up all the positive even numbers.
I think that’s interesting.
He knows that it may not be the only combination of primes that satisfy p1 + p2 = X for a given X. He also know that just finding two numbers that satisfy p1-p2 = 12n and add to 12x+10 doesn’t automatically make p1 and p2 prime.
Still, it’s a neat framework to think about the problem.
armstrongm, you’ve said multiple times, here and in other threads, that you understand mathematics, but that you just have a difficult time expressing it. But this is a contradiction. Mathematics is all about expressing things. That’s what it is. It’s a language. If you can’t say things in a language, then you don’t know that language.
I disagree (though not completely—there’s some truth here). Mathematics isn’t just a language; it’s also the content of what you express with that language. The set of great mathematcians is not identical to the set of great expositors of mathematics.
That’s not true. That’s not even close to being true. I can express myself but it’s not easy to do it when I don’t get asked questions and am only criticised
You think you have, because you’ve just done your A-levels and are off to university next year, so obv are ready to take on the Goldbach conjecture - Number theory is a young man’s game afterall Reality is that you’re not even wrong, so no one can answer your ‘question’ in any meaningful sense.
Go to university, get your head down for 4 years, and if you’re really, exceptionally brilliant, you still won’t even be wrong about the Goldbach conjecture. Pursue your studies beyond that, to PhD level, and it’s possible you may get to say something original about the GC. You will have achieved wrong-ness, which is not to be sneezed at.
I asked if it was new and relevant which I never got answered.
It would be wrong to think that I could solve such a conjecture of course it would. I am not naïve I understand that. I will never prove that conjecture true or false I don’t think I’m not that good. But you can’t tell me whether its new or not? It shouldn’t be that hard surely. Especially when one considers how simple it is.
Number theory is a young mans game it requires the creativity, brashness and boldness with knowledge that come from someone who is young. It comes from someone who it not weighed down by tradition and society. I often say god gave me one talent which is to spot patterns which is how this all came about. I’m not brilliant at anything else really.
The notion that mathematics is strictly a young person’s game is exaggerated:
Louis de Branges de Bourcia proved an important conjecture at 54.
Yitang Zhang proved an important conjecture at 58.
Someone with more free time than me can look through this list of mathematical discoveries and tell us some more examples of mathematicians making important discoveries later in life:
Plenty of other posters have already told you that expressing numbers as members of modular equivalence classes is not new. As for whether it’s relevant, well, I suppose it might conceivably be so, in the sense that anything in mathematics might conceivably be relevant to any particular problem, but you haven’t given us any reason to expect it would be.
Reality is that you’re not even wrong, so no one can answer your ‘question’ in any meaningful sense.