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From: Archimedes Plutonium on 12 Jul 2010 14:54


Archimedes Plutonium wrote:
> Archimedes Plutonium wrote:
> (snipped)
> >
> > There maybe a sticking point about this proof procedure for large even
> > numbered
> > prime pairs such as say p_n and p_n+1000, that we may have to have
> > some
> > more qualifiers to impose the Square Root Patch, due to the large
> > spread between
> > the n and even numbered n_
> >
>

Let me try this on a proof of the Infinitude of N+6 Primes:

Let me write a list of the first few primes:


2, 3, 5, 7, 11, 13, 17, 19, 23, . .


The first twin primes is 3, 5


The first quad primes (n+4) is 3, 7


The first (n + 6) primes is 5, 11


The first (n +8) primes is 3, 11


etc etc


And so it matters not, how large the N+2k becomes, because the
square-
root
patch on the last prime in the successive prime list captures all the
primes
of that succession, that finite succession, for example, doing the
N +6 primes proof would go like this:


Proof of the Infinitude of N+6 Primes:


(1) Definition of prime
 (2) Hypothetical Assumption, suppose set of all N+6 Primes is finite
 with
 5,11 being the last two N+6 primes of the sequence set S = 5, 7, 11
 where
 11 is the last and largest of the N+6 primes. Note we have to
eliminate
3 from the S succession list the prime factors of the 6/2 in N+6 so we
delete
3.
 (3) Multiply the lot and add 3 and subtract 3, yielding  W+3 =
(2x5x7x11) +3 = 773 and
 W-3 = (2x5x7x11) -3 = 767
 (4) Take the square root of W+3 and I get 27.8.... I do not need
square root of W-3, and there cannot be any
 regular primes
 for consideration of being a prime factor of this S secession that is
greater
than 27
 (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

And this is where I may get into new trouble, in that I cannot
eliminate them
and that the method would then only be a proof of the Infinitude of
Twin Primes
and that the proof of N +2k Primes has to await another method.

And the only reason that Twin Primes is amenable to this method is
because of the
separation of just 2

So it is an open question at this moment whether the method is
restricted to a proof of
Twin Primes but no larger N+2k primes.


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
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