
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 UTC5, Archimedes Plutonium wrote: > Alright, let me begin making lists: > >
Of course we have 1+1=2
> > 1+4 =5 and we have 41=3 > > > > 4+9=13 and we have 94=5 > > > > 25+4=29 and we have 169=7 > > > > 25+16=41 and we have 3625=11 > > > > 49+4=53 and we have 4936=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 APPostulate that between successive perfectsquares 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 perfectsquares 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 perfectsquares 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(perfectsquare) +0 and deleting all nonprimes.
My conjecture is more substantial in that I have Prime = Perfectsquare_1 + or  Perfectsquare_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{

