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Old 2019-03-25, 20:59   #1
MathDoggy
 
Mar 2019

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Default I Think I Have A Proof of the strong Goldbach conjecture

Introduction: The Goldbach conjecture is a mathematical supposition which was formulated by Christian Goldbach in 1742 in a card to Leonhard Euler. What the conjecture states is that every even number greater than 2 can be expressed as the sum of two prime numbers.


Proof by direct method:
( A even semiprime number is a positive integer which is even and can be expressed as the sum of two prime numbers)
Let k be the infinite sum of the first n even semiprime numbers
Let x be the infinite sum of the first n natural numbers
Let k>x
Let k,x > 0

Lets asume that the infinite sum of the first n semiprime numbers converges into a last semiprime number.

Now lets us check by the comparison criterion whether the infinite sum of the first n semiprime numbers diverges or converges.

First let´s prove the divergence of x so that it implies the divergence of k

x= 1+2+3+4+5+6+7+8+9+10+11...
Now I will choose the largest power of 2 that is less or equal to N, where N represents the numbers distinct from 2
Now we have, x= 0+1+2+2+2+2+3+3+3+3+3...
Obviously the limit of this series diverges, therefore x diverges, and finally k diverges
so we can conclude that there does not exist a last even semiprime number.
Q.E.D

Last fiddled with by MathDoggy on 2019-03-25 at 21:01
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Old 2019-03-25, 21:17   #2
R. Gerbicz
 
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Good work, move to the Riemann conjecture.
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Old 2019-03-25, 23:29   #3
MathDoggy
 
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Thank you
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Old 2019-03-26, 02:21   #4
CRGreathouse
 
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Old 2019-03-26, 05:34   #5
LaurV
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Theory of the k-camel.

Let's define a k-camel as to be a camel with k humps.

Examples: a 2-camel would be a bactrian, a 1-camel would be a dromedary, and a 0-camel would be a llama. Or a horse. Here the scientists didn't decide yet. Atempts were made to define a 0-camel as a cow, but those failed miserably, and not because cows cause global warming. (For those who don't know, there are species of Asian cows with humps).

One of my former uni professors developed this theory. He was a genius. Somehow I lost the connection with him for years, and I don't even know if he is still alive... Shame on me. What a pity it does not sound so funny in English, because you don't really have the "cacophony" concept. (explanation: in Romanian, as well as in other related languages, not only Romance, but Greek too, etc, we have this, from where the name came into English, actually, and it is considered rude to put together words in that way in speech or writing, therefore some people go to endless roundabouts to avoid it, which sometimes sounds very VERY funny).

In original (and for few who know Romanian here): "o k-cămilă este o cămilă cu k cocoașe". Etc. (we pronounce k like "kah" as in "car" or "carp") (edit 2: actually google translate does a very good job of pronouncing it, click the link and click "listen" - the small speaker below the text, ignore the translation which is wrong, the bot doesn't know the plural of "cocoașă"=hump, and don't use hyphens, the pronunciation will be worse)

This theory was consistent and complete (no joke! with axioms, theorems, demonstrations, etc), and it could be used to demonstrate anything. I mean, ANYTHING. He presented it to us once, and we were under the desk rolling on the floor with laughing.

Somehow I was so dumb and I lost the papers, and I can only remember it partially. Any attempt to reconstruct it along the years failed, my theory still has a lot of gaps.

Should I make more efforts to reconstruct it? Maybe it should be useful right now... ?!

Last fiddled with by LaurV on 2019-03-26 at 06:06 Reason: links, spaces
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Old 2019-04-12, 01:01   #6
MathDoggy
 
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Quote:
Originally Posted by MathDoggy View Post
Introduction: The Goldbach conjecture is a mathematical supposition which was formulated by Christian Goldbach in 1742 in a card to Leonhard Euler. What the conjecture states is that every even number greater than 2 can be expressed as the sum of two prime numbers.


Proof by direct method:
( A even semiprime number is a positive integer which is even and can be expressed as the sum of two prime numbers)
Let k be the infinite sum of the first n even semiprime numbers
Let x be the infinite sum of the first n natural numbers
Let k>x
Let k,x > 0

Lets asume that the infinite sum of the first n semiprime numbers converges into a last semiprime number.

Now lets us check by the comparison criterion whether the infinite sum of the first n semiprime numbers diverges or converges.

First let´s prove the divergence of x so that it implies the divergence of k

x= 1+2+3+4+5+6+7+8+9+10+11...
Now I will choose the largest power of 2 that is less or equal to N, where N represents the numbers distinct from 2
Now we have, x= 0+1+2+2+2+2+3+3+3+3+3...
Obviously the limit of this series diverges, therefore x diverges, and finally k diverges
so we can conclude that there does not exist a last even semiprime number.
Q.E.D
Instead of the infinite sum of the n first semiprime numbers it is the infinite sum of the semiprime numbers and the same thing is applied to the infinite sum of the natural numbers
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Old 2019-04-12, 02:04   #7
retina
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Quote:
Originally Posted by MathDoggy View Post
... the infinite sum of the n first semiprime numbers ...
A finite set of n things can only sum to infinity if infinity is one (or more) of the elements. Show me a semiprime number that is infinity.

Last fiddled with by retina on 2019-04-12 at 02:10
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Old 2019-04-13, 15:55   #8
MathDoggy
 
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I can't
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Old 2019-04-13, 16:03   #9
retina
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Quote:
Originally Posted by MathDoggy View Post
I can't
So then go and fix your proof.
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Old 2019-04-13, 16:13   #10
MathDoggy
 
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I will
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