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From: Transfer Principle on 24 Jul 2010 00:00
On Jul 23, 5:11 pm, "sttscitr...(a)tesco.net" <sttscitr...(a)tesco.net>
wrote:
> > Tonio, aka the third human to first do something Archie said.
> > (Again, please: who was the second one?)
> Archie Poo believes that the only human ever to agree with him is, I
> think, Karl Heuer, a mysterious and enigmatic character. Probably,
> one of Archie Poo's multiple personalities actually intelligent
> enough to read and write.

A Google search for Karl Heuer reveals several old posts back
from AP's earliest days at sci.math. In October 1994, Heuer
commented on AP's proof thusly:

"Under the assumption that 13 is the largest
prime, <59, 509> cannot be the prime factorization of 30031
because its components are too large to be primes.

"Anyway, my point was that if someone proves ~A -> B as the first step
and
then derives a contradiction, thus proving A, this is not inconsistent
with
the observation that other people have proved A by beginning with the
step
~A -> ~B.

"Personally, I've always thought that the usual form of the proof (I
don't
know how closely it matches Euclid's wording) is inelegant due to the
two
unnecessary uses of the law of the excluded middle."

Of course, one would think that someone opposed to LEM would be
opposed to reductio ad absurdum as well, but we see that Heuer
wasn't necessarily opposed to LEM, but merely preferred a proof
not using LEM to one that does.

According to the Google archives, Heuer's first Usenet post was
all the way back in 1989 -- predating AP by four _years_. Thus,
to me, it's no more likely that Heuer is an alter ego of AP than
for sttscitrans and Tonio to be the same poster. Furthermore,
his first post asked about generalizations to the Four Color
Theorem and has nothing to do with any of AP's ideas.

Meanwhile, Heuer's final post was in 1998, to gnu.emacs.bug, so
it's understandable that neither sttscitrans (whose first post
was six months after Heuer's last post) nor Tonio (whose first
post was in 2004) would be familiar with Heuer.
From: sttscitrans on 24 Jul 2010 04:26
On 24 July, 04:41, Transfer Principle <lwal...(a)lausd.net> wrote:
> On Jul 23, 1:00 pm, Archimedes Plutonium
>
>
> Regardless of whether sttscitrans is correct that AP considers 1 to
> be prime, we note that AP does implicitly use the fact that 1 and -1
> are the only units anyway. For if p_1, ... p_k are taken to be
> _positive_ primes, then W must be greater than or equal to 1

Yes, but AP claims to have a VALID indirect proof,
not just to have made a correct statement about W+1.

If 1 is a prime number then the supposition
that the primes are finite leads to no
contradiction. GCD(w,w+1) = 1, a prime.
The fact that w and w+1 cannot share any
prime factors is crucial.

AP claims that w+1 is "necessarily" prime
and by this means that w+1 cannot be a unit or a
composite, so indicating the existence of a "new"
prime.

If PRIMES = {3,5}
you have the following prime factorizations

1 = (0,0)
2 = (0,0)
3 = (1,0)
4 = (0,0)
5 = (0,1)
6 = (1,0)
7 = (0,0)
..
15 = (1,1) = w
16 = (0,0) = w+1

It is true that gcd(w,w+1) =1
But as 16 has proper divisors,
it cannot be prime.

A number is prime is it has no proper divisors.

Surely the correct deduction is that
16 has no prime divisors and this contradicts
unique factorization as 16>1.

This deduction is also true if you choose
PRIMES = {2,3,5)

30 = (1,1,1) = W
31 = (0,0,0)= w+1

GCD(30,31) = (0,0,0), i.e. the same empty
prime factorization as 1 =(0,0,0)

Can you validly deduce that w+1 is prime or
composite, if it has no prime fcatorization whatsoever
i.e. is a unit > 1.

GCD((1,1,1), (a,b,c)) =(0,0,0) => n= (0,0,0)






From: Tonico on 24 Jul 2010 04:26
On Jul 24, 6:41 am, Transfer Principle <lwal...(a)lausd.net> wrote:
> On Jul 23, 1:00 pm, Archimedes Plutonium
>
>
>
>
>
> <plutonium.archime...(a)gmail.com> wrote:
> > Archimedes Plutonium wrote:
> > > Not modify; and let me say, to render the valid proof indirect. All
> > > other attempts of Indirect on Euclid Numbers were invalid proof
> > > arguments because only when P-1 and P+1 are necessarily new prime
> > > numbers is there a valid Euclid IP Indirect proof. So I am not
> > > modifying anything, I am rendering the first valid Euclid IP
> > > Indirect. And why would any intelligent mathematician, knowing that
> > > Regular Primes infinitude is a more general theory than just the
> > > subset of Twin Primes, why would any mathematician with his/her
> > > thinking cap on, think that the Euclid method cannot yield Twin
> > > Primes when it yields Regular Primes.
> > (1) definition of prime number
> > (2) hypothetical assumption, assume the primes are finite and that
> > the sequence list is 2,3, 5, 7, 11, . . , p_k
> > (3) multiply the lot and add 1, calling it W+1
> > (4) W+1 is necessarily a new prime because of definition in (1)
> > joining with the fact that
> > division of W+1 by all the primes that exist in (2) leave a remainder
> > (5) contradiction to (2) that p_k is the largest and last prime, for W
> > +1 is now the largest prime
> > (6) reverse supposition step (2) and primes are infinite
> > LWalk, all you have to do to become the third human to have done a
> > valid Euclid IP Indirect and the only humans to do a valid Indirect,
> > since all Indirect Euclid IP has to have W+1 as necessarily prime.
> > All you have to do LWalk is agree that the above is a valid Euclid
> > Indirect.
> > Just say yes, and then I will count you as the third human being to be
> > able to do a valid proof indirect.
>
> So AP is asking me to settle the dispute between himself and the
> anonymous poster (on Google, he appears only via the email address
> sttscitr...(a)tesco.net) regarding Euclid's infinitude of primes proof.
>
> In particular, according to AP, if we assume that there are only
> finitely many primes and W is their product, then W+1 must necessarily
> be a prime number. But according to sttscitrans, W+1 must necessarily
> _not_ be prime.
>
> And so which side do I believe is right? Answer: _both_ are right!


Of course they are! What else could you have judged? And Had you been
asked about who's right in something out of 100 people you'd judged
they all are right, too...what else?

Anyway, I robbed you the glory to become the third human to first do
something impressively important that AP said.
Sorry and suck it up.

Tonio
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