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 #2020 Correcting Math

Posted: Sep 4, 2014 3:49 PM

On Thursday, September 4, 2014 3:57:51 AM UTC-5, Archimedes Plutonium wrote:
> Perhaps I should not give up so quickly that the primes have no general formula that delivers all primes.
>

(snipped)

>
> > 1+1 = 2
>
> >
>
> > 4-1 = 3
>
> >
>
> > 9-4 = 5
>
> >
>
> > 16-9 = 7
>
> >
>
> > 36-25 = 11
>
> >
>
> > 9+4 =13
>

Alright, the conjecture looks to be true, in that I have not found any counterexample.

The 10th prime is 29 and the 10th perfect-square is 100

Now, how far out do I need to go to find the first and perhaps only 29 = p-sq_1 + or - p-sq_2

Well it happens that 225-196 = 29

However, 29 = 25 +4

So I need to discard the idea of 1-1 correspondence because it is somewhat clear that we have a sort of oscillation like a trig function of add or subtract. Perhaps even a harmonic oscillation.

Now it is clearly known that the primes are more abundant than the perfect-squares because we have to go to 100 for the 10th perfect square yet only 29 for the 10th prime. So I can forget or discard the idea of 1-1 correspondence of prime to perfect square.

Now the subtraction appears to give me many primes, but does the addition give me as many?

AP