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From: Archimedes Plutonium on 8 Aug 2010 17:05
I posted versions of the below sometime in the mid 1990s, perhaps
1996 is the earliest.
--- quoting from old post of mine of the mid 1990s ---
My earlier proof of 1991-1993 was and still is correct and the
world's
quickest proof of this theorem. In the early 1990s I had sent my
proof
to Notre Dame University to a professor there to assess my proof and
below is her reply. I feel and still feel very strongly that the
referees at Notre Dame were incompetent. I shall repeat my proof of
the
Infinitude of Twin Primes below.

---quoting a reply to my Infinitude of Twin Primes to a Notre Dame
journal of logic---


         UNIVERSITY OF NOTRE DAME
                DEPARTMENT OF MATHEMATICS
                                                                Aug.
6
Ludwig Plutonium
P.O. Box 851
Hanover, NH  03755


Dear Mr. Plutonium,
        Your paper entitled "Logical corrections to the proofs of
the
infinitude of primes" is not accepted for publication in the J.S.L.
 I
enclose a copy of the referee's report.
                                                        Yours truly,
                                                (signed) Julia F.
Knight
        Department of Mathematics, University of Notre Dame, Mail
Distribution
Center, Notre Dame, Indiana 46556-5683* Phone 219 631-7245


Report on "Logical corrections to the proofs of the infinitude of
primes", by Ludwig Plutonium


This paper should not be published. Every working mathematician knows
a
correct proof that there are infinitely many primes. The proposed
proof
that there are infinitely many twin primes, with its vague appeal to
symmetry, is nonsense.
--- end quoting ---


Proof of the Infinitude of Twin Primes: suppose false then P_k and
P_k+2 are the final and last two twin primes. Construct the numbers
((2x3x5x7x.... P_k x P_k+2) +1) and ((2x3x5x7x.... P_k x P_k+2) -1).
These two new numbers are necessarily prime given the restricted
universal set of primes under the supposition. Contradiction hence
infinitude of twin primes.


Example: suppose 5,7 were the last and final twin primes and thus no
more primes exist. Construct ((2x3x5x7) + 1) and ((2x3x5x7) - 1)
yielding 209 and 211. Now, in this restricted universal space of
primes
where 5,7 are the last and final primes in existence, then by the
Force
of Logic 209 and 211 are new primes not on the original list. Even
though we know they are not twin primes when we look at them outside
of
the rigors of this Reductio Ad Absurdum. Euclid's very own proof of
the
Infinitude of Primes does the very same thing in guaranteeing that
his
new number is a prime under the rigors of the supposition. So what
the
Euclid Infinitude of Primes proof gives is not just one new prime
not
on the original list but in fact Twin Primes. And hence the
Infinitude
of Twin Primes.


The trouble with Notre Dame logic journal is that none of them were
competent enough in the early 1990s to evaluate the above which is
the
world's first proof of the Infinitude of Twin Primes.


The reason I bring up this topic just now is because a few days ago I
was talking about the fact that given Moebius theorem is such a
strong
fact of 4 mutual adjacencies is the maximum in the plane that such a
strong fact creates a short and fast proof of 4 Color Mapping. Now
we
look at Euclid's Infinitude of Primes and we notice that the
symmetry
that plus 1 or minus 1 to multiply the lot yields not just one more
new
prime but yields Twin Primes. And so this fact is another one of
those
very Strong facts that leads to other proofs such as Twin Primes.


I must say one nice thing about Notre Dame in that they did notice
"symmetry" of my argument, which is very true. But sadly, Notre Dame
did not have the brains to realize that my submission was the
world's
first proof of Infinitude of Twin Primes.

--- end quoting my mid 1990s post to sci. math about Infinitude of
Twin Primes proof ---

Now, what does Chandler Davis and Julia F. Knight have in common? What
they have
in common is that both are unable to do a Euclid Infinitude of Regular
Primes proof that is
a valid reductio ad absurdum (indirect method) proof. Neither Chandler
Davis nor Julia F. Knight and the reviewers (referees) of Journal of
Logic are unable and incompetent to do a
valid Euclid Infinitude of Primes Indirect method. If either Chandler
Davis or Julia Knight could
do a valid Euclid IP proof, they would immediately see that they can
thence do a Infinitude of Twin Primes proof.

As what Michael Hardy and Catherine Woodgold and Chandler Davis
excoriated Devlin's talk on the Euclid Infinitude of Primes proof in
the Fall 2009 magazine article shows that neither
Hardy/Woodgold/Davis have a proper handle on a valid Indirect Euclid
IP.

The reason, and only reason that Infinitude of Twin Primes was never
proven until the 1990s is because no-one before the 1990s ever did a
valid correct Euclid Indirect IP. No-one had enough good and proper
symbolic logic under their belts until the 1990s. No-one had a inkling
of how flawed their mishmeshed Euclid IP was, mixing up both the
contradiction and the constructive method all into one proof that
comes out invalid.

So why no-one able to prove Twin Primes? The answer is obvious and
clear, for no-one could even do a proper valid Infinitude of Regular
Primes. Once you can do a valid correct Regular
Primes with reductio ad absurdum, by symmetry you can easily do the
Twin Primes.

So I challenge both Chandler Davis and Julia Knight to post their
Euclid Indirect Infinitude of
Regular Primes. I doubt they can ever do a valid proof and I am here
to help them should they
make a mistake.

Even include Michael Hardy, although he is far from his field of
expertise of statistics and
Catherine Woodgold, she coming from electrical engineering, to post
their versions of Euclid IP Indirect and I am here to help if any
mistakes are made.

So, ladies and gentlemen, post your versions or are you too scared of
the truth that you are incompetent to do so.

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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