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From: Archimedes Plutonium on 20 Jul 2010 12:28

Based on the below post I should number this post
as 4.01 so as to squeeze this thread into my book:

From: Archimedes Plutonium <plutonium.archime...(a)gmail.com>
Newsgroups: sci.math,sci.logic
Subject: Wikipedia's flawed IP and here is how it should read #4; 2nd
ed;
Euclid's Infinitude of Primes Proof Corrected
Date: Sat, 22 Aug 2009 23:15:41 -0700 (PDT)
--- end quoting old post ---

Now then, recently David Tribble posted the below:

Archimedes Plutonium wrote:
> David R Tribble wrote:
(snipped)
> >
> > W-1 is not necessarily prime.
> > Consider 2 x 3 x 5 x 7 - 1 = 209 = 11 x 19.
>
> Yours is direct.
>
> Indirect, W-1 and W+1 are always necessary new primes, but do not feel
> bad because most
> mathematicians never got that correct either.
>
> That is why Twin Primes was never proved


So David still does not understand the Indirect Method and my answer
to him should have been more crisp and better explained. I should have
gone into more detail.

So let me do that here and now.

David, in the Indirect we have

(1) Definition of prime
(2) Suppose 2,3,5,7 are all the primes that exist where
7 is the largest
(3) form P-1 and P+1 which are 209 and 211
(4) both are necessarily new primes because 2,3,5,7 are the only
existing primes given the hypothetical supposition and by definition
of prime 209 and 211 are
indeed primes in this space
(5) contradiction that 7 is the largest prime
(6) primes are infinite

So you see David Tribble and Chandler Davis, that no matter what
primes you list for the supposition step, the hypothetical supposition
step, the definition of prime in conjunction with the fact that a
division leaves a remainder will give you twin primes necessarily in
this method.

If 3 and 5 are the only primes in existence, then the definition of
prime and the Indirect Method entails that
14 and 16 are necessarily two new primes in this space.

Now I am including Chandler Davis of Mathematical Intelligencer since
by email he also is like David Tribble in not understanding how the
Indirect method works and delivers Infinitude of Twin Primes proof.

Of course, in the Infinitude of Twin Primes, in the Indirect the twin
primes are not numbers like 14,16 nor are they numbers like 209 and
211, but in the proof
schemata, they are a pair of generalized twin primes as
P-1 and P+1.

And Twin Primes are infinite because once I do a proof of one pair say
P-1 and P+1, I throw that pair into a recursive second proof and yield
out Q-1 and Q+1, and
the recursion goes on infinitely many times.

So what the Chandler Davis's editing of Hardy/Woodgold article in
Mathematical Intelligencer without due reference to Archimedes
Plutonium's work that preceded Hardy/Woodgold by 2 decades, is the
recognition of Chandler Davis that not only did the math community not
understand whether Euclid's proof was constructive or contradiction,
but they failed more
importantly to see that Euclid's Indirect is a proof of the Infinitude
of Twin Primes.

Chandler, from his email, fails to recognize that P-1 and P+1 are
necessarily new primes in that method.
And the only reason Twin Primes was never proven before, is because no-
one had a valid Indirect Method
in their head.

And David Tribble seems not to recognize that the Structure the
framework of logic of the method yields
two new primes, no matter what example he throws up.
David seems oblivious to the idea that if 3 and 5 are the only primes
to exist, it is the method that forces 14 and 16 in this hypothetical
space are also primes. And then, when you do it on "generalized
numbers" of P-1 and P+1, that they truly are two new twin primes from
any finite supposed list of all primes.

Mathematicians are supposed to be more logical than anything else, but
when it comes to Euclid IP indirect, they seemed to have melted away
in the hot summer sun of pointing to irrelevant examples.

And I do not know how old Mr. Chandler Davis in Toronto is, whether he
is too old to want to change and learn a correct Indirect Euclid IP or
whether Chandler ever penned a Indirect Euclid IP.
I do know that David Tribble is not a mathematician and doing this out
of sheer curiosity and so if David can understand that P-1 and P+1 are
necessarily two new primes in the Indirect, then Chandler Davis, the
editor of Mathematical Intelligencer should be able to see that these
are two new primes and that they are the key to a Infinitude of Twin
Primes proof.

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
From: spudnik on 20 Jul 2010 14:06
how can your proof be sufficient, if there is not enough
of a characterization of primes to exclude 3x5 +- 1, or
of 209? (not sumorial.) I mean,
it's sort of like the sieve of Eratosthenes,
constructed with big holes (2, 3, 5, 7, 209, 211), and
you did not construct the first-four primes,
only assumed them ... so,
how could such proving, prove any thing?

anyway, if there is some sort of isomorphism
between inductive & deductive proof, if
they lead to the same statement, then
there is probably a simple way to exchange them
-- and I hav read it in *Mathematics Magazine*.

--BP's Waxman's cap&trade, on the docket
pour lees ducs d'oil -- the next (last?) Bailout!
http://tarpley.net
From: sttscitrans on 20 Jul 2010 21:46
On 20 July, 17:28, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> Based on the below post I should number this post
> as 4.01 so as to squeeze this thread into my book:
>
> From: Archimedes Plutonium <plutonium.archime...(a)gmail.com>
> Newsgroups: sci.math,sci.logic
> Subject: Wikipedia's flawed IP and here is how it should read #4; 2nd
> ed;
>         Euclid's Infinitude of Primes Proof Corrected
> Date: Sat, 22 Aug 2009 23:15:41 -0700 (PDT)
> --- end quoting old post ---

Unfortunately, it is AP that cannot keep
"indirect" and "direct" apart.
As AP cannot reason in the astract, he lets
his "computational experience" prevent him from
making correct deductions.

Perhaps a concrete example more suitaed to
AP's limited intellect will help him see the
error of his ways.

Imagine a hotel which is simply an unending row of rooms with a first
room and no last room, each room being capable of accommodating any
number of guests.

Each guest has a copy of the Rules of the Hotel,
which are:

1) The only guests allowed into the hotel
are Americans, Germans or Estonians
2) Every room, except the first, contains a unique
combination of guest nationalities
3) Every combination of guest nationality is found in
one and only one room
4) No two guests in immediately adjacent rooms have
the same nationality.

By 3) There is one and only one room, call it room W, that contains an
American, a German and an Estonian.

Relaxing in room W, the German, a logician,
begins to wonder who is next door.
"Rule 2) tells us that there must be guests
on both sides but as there is an American, an
Estonian and a German in this room, by rule 4
there must be a guests of some other nationality
in the two rooms next to ours. But that
contradicts rule 1). The only nationalities
allowed in the hotel are Americans, Germans
and Estonians". "No", says the Estonian. "We
could be on the immediate right of the first room -that's empty. So we
must be in the second room along".
"But who's in the third room?" asks the Estonian.

Archie Poo the American then says "Don't you see
if the third room contains neither an American nor
a German nor an Estonian, then by rule 2, the guest in
the room next door is necessarily Italian.
"But what about rule 1" shout the others.
"There are no Italians in the hotel".

Archie Poo is very, very, very stupid, belives
that everything he says must be right and
simply repeats ad inf what he has said before.
Babbling about twin prime conjectures, the Riemann
hypothesis and such like.

So who is/are in room w-1 and room w+1 ?
Could it be an Aztec or a Roman ?

Say each guest is assigned a prime number

Americans = 5
Germans = 2
Estonians 7

The AGE group is assigned room No 2x5x7 = 70
Room w-1 has the number 70-1 = 69 = 3x23
Obviously no guest has the number 2 or 23

Only Archie Poo thinks what you have
deduced using the "rules of the hotel" can
be applied to the naturals





From: sttscitrans on 21 Jul 2010 11:08
On 20 July, 19:06, spudnik <Space...(a)hotmail.com> wrote:
> how can your proof be sufficient, if there is not enough
> of a characterization of primes to exclude 3x5 +- 1, or
> of 209? (not sumorial.)  I mean,
> it's sort of like the sieve of Eratosthenes,
> constructed with big holes (2, 3, 5, 7, 209, 211), and
> you did not construct the first-four primes,
> only assumed them ... so,
> how could such proving, prove any thing?

If you are assuming that 3 and 5 are the only primes
then the set of primes, PRIMES = {3,5}.

Consequently, the set of nonprimes must be
NONPRIMES = {1,2,4,6,7,8,......} =N\PRIMES

The definition of prime in this case is
n is prime if it has precisely two distinct divisors
and belongs to PRIMES.


7 is a nonprime. It has precisly two distinct
divisors (1,7) but 7 does not belong to PRIMES.

AP thinks that there are naturals that can be
simultaneously in PRIMES and NONPRIMES.

PRIMES = {2,3,5}
NONPRIMES = {1,4,6,7,8,9,10, ...}

2x3x5+1 = 31. 31 has two and only two distinct divisors
but 31 is not an element of PRIMES.

8 is a nonprime. It has four distinct divisors
(1,2,4,8)

GCD(3x5,3x5+1) = GCD(15,16) =1

All this means is that neither 3 nor 5 divides 16.
Two consecutive naturals do not share any common factors other than 1

This is true as
16 = 1x16, 2x8, 4x4, 2x2x2x2

16 is not prime, neither is it a product of primes.
If it were prime, it would be in PRIMES

Of course, in the naturals every n>1 has at least
one prime divisor, so the set of PRIMES
in the naturals cannot be {3,5} or any other
finite set of primes.

From: Transfer Principle on 22 Jul 2010 23:00
On Jul 20, 9:28 am, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:
> Archimedes Plutonium wrote:
> > David R Tribble wrote:
> (snipped)
> > > W-1 is not necessarily prime.
> > > Consider 2 x 3 x 5 x 7 - 1 = 209 = 11 x 19.
> > Yours is direct.
> > Indirect, W-1 and W+1 are always necessary new primes, but do not feel
> > bad because most
> > mathematicians never got that correct either.
> > That is why Twin Primes was never proved
> So David still does not understand the Indirect Method and my answer
> to him should have been more crisp and better explained. I should have
> gone into more detail.

I notice that both JSH and AP are working on the Infinitude
of Twin Primes, but via different methods. JSH is looking at
congruences mod various primes, while AP is attempting to
modify Euclid's proof so that it works for Twin Primes.

Meanwhile, the following isn't directly related to Twin
Primes, but I post it here anyway. In another thread, I
pointed out that today, the 22nd of July, is known as Pi
Approximation Day since pi is approximately 22/7.

The question asked in another thread was, does AP believe
that pi is _approximately_ 22/7, or _exactly_ 22/7?

(If the former, then maybe he considers today to be Pi
_Exactness_ Day...)
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