Prev: a second patch onto the square-root patch?? #654 Correcting Math
Next: Why did I Embrace Islam?
From: Archimedes Plutonium on 12 Jul 2010 15:43
>
> Now what could save the above:
>
> (5) Successively divide all the primes in the sequence S into W+3
> and W-3 and they all leave a remainder but I also need to consider
> primes from
> 11 out to 27 and they are 13, 17, 19, and 23
>
> Is that somehow, if 13, 17, 19, and 23 were prime factors of W+3 = 773
> and
> W-3 = 767 then 2, 3, 5, 7, 11 would also be a prime factor of W+3 and
> W-3
>
> So there is still hope that the Euclid Indirect of Euclid's Number
> necessarily prime
> captures not only the Twin Primes infinitude proof but captures all
> even numbered Primes
> infinitude proof.
>
> I am still hopeful that another patch can wrangle out the pesky
> regular primes that look
> to interfer
>

Ironic, how I excoriated others for mixing two methods in a proof of
Euclid's IP
when I committed the same error above, jumping back and forth between
the
indirect and into a direct.

The method above works for Twin Primes, but unsure of whether it can
work for
N +2k where k >1.

The key aspect of the Indirect proof is that all the primes that exist
are supposed
in that Succession. Can I say that W+2 and W-2 for N+4 Primes or that
W+3 and W-3 for N+6 Primes are all the primes that exist in Succession
S.

Nay, I think not. I can obviously say it for twin primes since I can
be assured
no prime sneeks between twin primes. Can I say it for N+4 primes? I
think yes
I can say it for them also that the method works because I have a
proof that
3,5,7 is the unique and no other such prime set.

How about N+6? Can I say that 3,5,7,11,13 is unique to N+6 and thus
beyond
is a safe proof of N+6 Primes?

So maybe I can find a resolution in this manner by having to prove
before the N +6
Indirect method is to prove that only N+6 primes that could upset the
proof format
is the 3,5,7,11,13 sequence and as you go larger in the sequence of
Primes you cannot
squeeze a new prime between that of N+6 primes.

One thing is assured, I have a proof of Twin Primes infinitude, and
likely a proof of
Quad Primes infinitude. As to whether more proofs of N+2k are
forthcoming is an
open question.

Archimedes Plutonium
http://www.iw.net/~a_plutonium/
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
 | 
Pages: 1
Prev: a second patch onto the square-root patch?? #654 Correcting Math
Next: Why did I Embrace Islam?