Let me first start out by saying sorry if I spelled this great mathamatician's name incorrectly, I highly respect his work and mean nothing by it. Anyway, I had been first intruduced to this theory about 5 years ago when I was 11, and I had done much thinking about it, I spent countless hours working of something that would help further more explain his theory, I have only one equation from 5 years of pondering and I would like some ideas and suggestions about my equation. If some of you are not familiar with his theory, it states that the sum of any two prime numbers from 2 to infinite will equal an even number, for example the numbers 3 (prime number) and 5 (prime number) added toghter will equal 8 (even number). Yet the thing that is so impossible to predict and to prove further more is that numbers do not end, so 3+5=8 may be true yet it is impossible to tell if that will hold true for other larger numbers that are un-imanagable. This is Goldbach's Theorum (excuse me for the mistake in spelling) and has greatly to do with the Reaiman Hypothesis, but thats another disscussion all in its-self. Here is my formula towards the Goldbach Theorum: E = x1 + x2 = z (x = 2- n) Please note the x1and x2 are sub-scripts Domain: x1=first prime number x2=second prime number z= even number E=simation (computer wouldn't let me paste it) n=infinite Please leave any feed back that would help, I truly appreaciate any help that I can get from all your knowledge. Thank you, P.s. Andrey I finally found my password after 2 hours, lol, I really need cable.
Consider any prime three or greater. They must be odd numbers otherwise they would be divisible by two and not prime. If you add any two odd numbers together the result is even. This is based on modular arrithmetic. In bargain basement version A Mod B is the remainder after deviding A by B. If the A is negative this is done so that the answer is still a positive number. For example 0 mod 12 = 0 11 mod 12 = 11 12 mod 12 = 0 13 mod 12 = 1 -1 mod 12 = 11 -11 mod 12 = 1 -12 mod 12 = 0 -13 mod 12 = 11 11 mod 3 = 2 Now there is a theorum , (not too difficult to prove) ((A Mod N) + (B Mod N)) Mod N = (A+B) Mod N. You can use this to show If N is two. The if B is odd then B mod 2 = 1. If A is also odd then A mod 2 = 1. By the rule above (A+B) Mod 2 = 0. So A+B is an even number.
Hi! Allow me to clarify the statements above. Goldbach's Theorem is not about the sum of two prime numbers being even. That is obvious. Goldbach's theorem states that any even number can be expressed as a sum of two prime numbers. As far as my knowledge is concerned, that has not been proved yet for any arbitrary even number. So far no counterexample has been presented to debunk the theorem (i.e. all even numbers below some value satisfy goldbach's theorem).
Re: Re: Goldbach's Prime number Theorum Of course this is obvious ! Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! Odd numbers are of the form: 2n+1 (for all n > 0) And it´s obvious that prime numbers (except 2) are odd numbers. (Note that I don´t want to say that all odd numbers are prime!!!) Well... if you add two odd numbers you will get an even number: (2n+1) + (2n+1) = 2(2n+1) which is obviously even because it can be divided by 2. That´s all Cesar
wow goldbach conjecture at 11? jeez man i wish my parents/teachers were as involved... I also have been working on this problem...but then I skipped to the twin primes problem because my solution led me there ....I got somewhere but i won't show my results...its a generation of the twin primes list...still trying to prove that it produces the whole list. But anyhow i found this paper couple of month ago that you might like to see. Don't know if they really solved it but it says they did. FIND THIS ON GOOGLE: author: KAIDA SHI title: "a new method to prove the goldback conjecture, twin primes, conjecture and other 2 propositions" it may be a bit complicated for you but hell if you know this by 11 then it shouldn't bne too bad
The great thing about the internet is anyone can publish their work cheaply. The horrible thing about the internet is anyone can publish their work cheaply. That article is an example of a horrible thing. If you check out the Mathematics ArXiv site, you'll find some other 'outstanding' papers by Kaida Shi, including (but not limited to) proofs of the Riemann Hypothesis and Fermat's last theorem (note that it's not a requirement that an article on ArXiv is refereed).
true but its up to the reader to always judge even if the paper is refereed...especially in psychology there are alot of questionable papers out there that are found in journals.
Okay, for an eleven year old, a lot can be excused but it is dismaying that after 5 years of working on it, Mr. Dalal still seems to think that Goldbach's conjecture says that "the sum of two prime numbers is even". Goldbach's conjecture is, of course, that any even number can be written as the sum of two prime numbers. Quite a different thing. By the way, Goldbach was hardly a "great mathematician". He was an amateur who conjectured a great many things (many of them already proven false) but was never able to prove any of them himself.
