Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: professors of Stanford endorsing proof of Goldbach to arxiv
Replies: 20   Last Post: Sep 5, 2014 4:14 AM

 Messages: [ Previous | Next ]
 plutonium.archimedes@gmail.com Posts: 18,572 Registered: 3/31/08
Re: new Conjecture Primes the sum or subtraction of two perfect squares
Posted: Sep 4, 2014 9:39 PM

On Thursday, September 4, 2014 3:31:23 PM UTC-5, Archimedes Plutonium wrote:
> Alright, let me begin making lists:
>
>

Of course we have 1+1=2

>
> 1+4 =5 and we have 4-1=3
>
>
>
> 4+9=13 and we have 9-4=5
>
>
>
> 25+4=29 and we have 16-9=7
>
>
>
> 25+16=41 and we have 36-25=11
>
>
>
> 49+4=53 and we have 49-36=13
>
>
>
> So it looks like we get about as many additions to make primes as subtraction.
>
>
>
> Now I wonder if the Pythagorean theorem has some role in this conjecture because as we notice the square roots of perfect squares:
>
>
>
> 5+2=7 from sqrt25+sqrt4
>
>
>
> A proof of the Conjecture appears to be independent of the proof of Goldbach.
>

Independent but using a key aspect of the AP-Postulate that between successive perfect-squares lies at least two primes.

I am confident the conjecture is true, which leaves for a intriguing proof in that as the primes get larger the spacing between primes increases and the spacing between perfect squares increases. For example at 3 to 5 is a spacing of 2 units but at 23 to 29 is a spacing of 6 units. And for perfect squares from 4 to 9 is a spacing of 5 but at 81 to 100 is a spacing of 19.

The baffling part of the conjecture and its proof when forthcoming is how and why perfect-squares are related to primes. It is not at all obvious that perfect squares are aligned in some orderly fashion with primes.

Now there is a Trivial Conjecture of primes and perfect-squares if we admit 0=0^2 as a perfect square, so that if you listed all the perfect squares 1, 4, 9, 16, 25, etc etc and then you have a formula of Prime = sqrt(perfect-square) +0 and deleting all nonprimes.

My conjecture is more substantial in that I have Prime = Perfect-square_1 + or - Perfect-square_2

The proof is not going to be easy.

This conjecture seems to be an original conjecture for I see nothing remotely similar in the literature.

AP{