When people say the problem is not solved, what do they mean? What does it mean to prove the goldbach conjecture? If I arrive at a conclusion, how to prove this is it?
It posits that every even whole number succeeding 2 is the sum of 2 prime numbers.
I fail to understand this.
Take 12500 for instance: 12500/2=6250.
12500 is an even number and 6250 can be divided by 2, 5 and 10. That would mean it isn't a prime number.
I am bad at Math and it is not my area of expertise, so this might seem like a dumb question. Please don't be mean to me:)
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> The Goldbach Conjecture states that any even number greater than 2 can be expressed as the sum of two primes.
> The get is at 2000.
I'm a newbie to mathematics, so correct me if I'm wrong.
When I'm looking at the photo of the partitions of Goldbach conjecture on google, I found that all even numbers(except 2,4) on the list can be expressed as a sum of two twin primes.
For example,
(3,5,7),(11,13),(17,19) are twin primes
6=3+3
8=3+5
...
14=7+7/3+11
16=5+11
18=5+13/7+11
20=7+13
...
Since there are infinitely many even numbers, so there would be infinitely many twin primes if this is true.
But, I'm a newbie. So I've no idea how to prove it.
So, I first saw the word -'conjecture' in the very end of my maths textbook of class 9 (no one read that additional info pages, but I did !) There was an example of mathematical conjectures, which was none other than the Goldbach's conjecture.
Currently I'm in 12th class (High school senior) and has tried to do something in it time to time. And recently I was studying distribution of primes to find any pattern and also some other related stuff. I caught up once againa on this forbidden love, and it striked to my mind as if it is something that I may prove with diving deeper in creativity.
And now I think, I've discovered a proof ! It is rather short, and uses basic 10th class algebra and assumption along with one of the theorems of Euclid. I wasn't convinced so I read it again and again to find the mistake, but I can't.
So can it be the case that I really may have discovered it. It is not possible for me to believe as 297 years have passed and I'm just not convinced that no one ever thought to do it using simple 10th class algebra.
I've shared it to my maths teachers and if do get a nod from them, I may also post it here (it is only 4 pages though). I just wanna know what are your opinions on it ???
EDIT : "Two of the maths teachers I knew both approved it, but you know I wasn't still convinced and thus the whole day yesterday I tried to figure out the mistake and finally I caught it - it was ambiguity in the very last statement. Now, I've modified it to make it clear, but to do so I need to turn it into a 'hypothesis', or either prove it myself(which I certainly can't do right now). So, I've added it as a hypothesis with a note. And, I may post it to reddit hopefully by today itself."
EDIT 2 : "I've submitted the manuscript, and yes I figured out the little mistake (not really a mistake, but some vague terms that I later corrected), and that leads me to use a hypothesis to prove it. If someone can prove that hypothesis, then surely we'll have a rigorous proof, and I know that the hypothesis can't be proved using undergrad maths. Also, my paper has cleared preliminary checks and is now under editorial review**"**
So, I was with this problem since I was in class 9th, and now I'm about to finish class 12th. Just this simple idea came to my mind and I thought that it can be quite interesting. I'm mainly self-taught and come from low-middle income family and there is no mentor who can help me here in my school and nearby region. So, I just myself headed up to the web and submitted a manuscript to JAMS, not knowing that it is one-of-the-most-prestigious Journal. And, I got rejected but the reason was just that it doesn't meet acceptance standards.
So now, can you please review and comment upon my findings ( I know the paper is extremely simple, but I think that it might lead us to some new insight).
Please share you Honest Opinion.
Thanks in Advance 😁
Here's the link : Manuscript
Hola,
I am in a bit of a pickle, I need to do a Goldbach Conjecture function. Now I tried to solve this problem by whipping out my Java skills and coding it in Java in my head, but I think it might have translated to gibberish. I might have some hubris here, but I think my logic is sound, however my code seems to be dogshit. First of all unless the console went invisible, my code dosen't even fucking produce an output. Here is the line of logic I followed, found the highest prime less than the input and then basic arithmetic would solve it. n-Prime[p] would solve all my problems, however reality struck me when I ran the command into the console, it all went to shit.
https://preview.redd.it/3pvzoqo31zt61.png?width=935&format=png&auto=webp&s=e9c3a6381bbcf39151061586e303a8396a92caa8
Apologies if this has been asked before, but I remember seeing something previously about how an AI generated a very close to exact equation for something that we didn't have that close of an equation for.
Would it be possible to set up an AI such that it knows what prime numbers are, it knows what even integers are so it could find a relationship between the two, thus giving a big boost towards goldbach's conjecture.
'it seems more globally applicable...' was ironically the wrong choice of words. Rather 'we have the opportunity to perceive the problem as...' gets more to the heart of my concern.
Thank you all for chiming in! I've really enjoyed learning from your responses.
Are there any useful implications of Goldbach's conjecture? Does it tell us anything about the distribution of the primes? Is it only the nature of the problem and its difficulty that makes it interesting?
If the goldbach conjecture is indeed correct, does that mean that for any even number X, the chances they there will be a prime number somewhere between x and x/2-1=100%?
For which (if any) classes of rings can we disprove it? And for which is it presumed to be true?
I have been reading about Goldbach’s Conjecture and could not find the contrapositive of it. Goldbach’s Conjecture states that “Every even integer greater than 2 can be expressed as the sum of two primes.” If I write this as an if-then statement, I have “If an integer is even and greater than 2, then the integer can be expressed as the sum of two primes.” How could this statement be written as a contrapositive?
I do not see the sum of any given number in prime numbers. Do you?
How should I do that?
Unarchived from here.
The Goldbach Conjecture states that any even number greater than 2 can be expressed as the sum of two primes.
The get is at 2000.
