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From: Archimedes Plutonium on 21 Jul 2010 03:36
Hard for me to imagine, or should I say, refuse to imagine that only
two human beings
can do a valid Euclid Infinitude of Primes:

Karl Heuer gives a correct Euclid IP, indirect method

Sun, 20FEB1994, 21:05:13 GMT sci.math
INCONSISTENT PEANO AXIOMS AND MATH PROFESSORS
Lines: 36
Sender: k...(a)spdcc.com (Karl Heuer)

k...(a)ursa-major.spdcc.com (Karl Heuer) writes:

In article (5JChA8g2...(a)jojo.escape.de>

det...(a)jojo.escape.de (Detlef Bosau) writes:
>Ludwig.Pluton...(a)dartmouth.edu meinte am 18.02.94
>>det...(a)jojo.escape.de (Detlef Bosau) writes:
>>>Wrong. Your two numbers are not necessarily prime
>>NO, YOU ARE WRONG. Those numbers are necessarily prime, due to
>>UPFAT, all the primes that exist in the finite set leave a remainder
>>of 1.
>I'll give you a lesson of elementary arithmetics. . .

I really shouldn't bother to get involved in this discussion again,
but
Ludwig is right. In logical terms, his key statement is "if P is a
finite set containing all the primes, then prod(P)+1 is prime." This
is
a true statement.

Let's step through your alleged counterexample:

>consider your set of primes to be: {2,3,5,7,11,13}, as I assert 13 to be
>the largest prime. [. . .] Now, you made the assertion, that
> > > > (2x3x5x11x13) + 1 [=30031] must be prime.

Yes, it's true that if 13 is the largest prime, then 30031 is prime.
Do
you disagree with that assertion?

>As you stated before, there exists an unique prime decomposition of
>30031. This is 59x509. It could be easily shown, that 59 and 509
>both are prime.

If 13 is the largest prime, then 59x509 is not a factorization of
30031.

--- end quoting Karl Heuer's post of 1994 ---

I am going to list Karl Heuer, who was my favorite replyer of my posts
when I
first entered into the sci newsgroups in the early 1990s. I am going
to list him
because he well understands the proof of Indirect Method and how it
forces
"multiply the lot add 1" to be necessarily a new prime regardless of
the
numerical value. It is the logical framework of the indirect method
that forces
this number to be "prime" but which weaker minds can not get over the
hurdle
of a number like 30031 and which those weak-minds then cannot deliver
a
valid proof. So to see the logic by a different author is instructive
to young people.

Although Karl does not write out a full proof of Euclid IP, Indirect
method, it is
obvious that he sees the full mechanism of the proof. And, also,
considering the
fact that in this list of about 50 authors, only a handful of about 5
manage to
give a valid proof of Euclid IP.

--- end quoting old posts to sci. math ---

So the new standard in mathematics, since nearly
everyone, including most math professors gum up
Euclid's IP, that everyone should deliver both the
Direct alongside the Indirect Proofs.

And also, anyone that does a valid Euclid Infinitude of Primes
Indirect Method, knows
his/her proof is valid, provided they can do a Infinitude of Twin
Primes immediately afterwards.

Here are both in short-form:

Proof of Infinitude of Regular Primes
(1) definition of prime
(2) hypothetical assumption: suppose set of all primes is finite with
this as their
sequence list 2,3, 5, 7, . . p_k, where p_k is the last and final and
largest prime
(3) Multiply the lot and add 1, and call it W+1
(4) W+1 is necessarily a new prime for the reason of definition of
prime in (1)
and the fact that division by all the existing primes leaves a
remainder
(5) contradiction to (2) since W+1 is a new prime larger than p_k
(6) reverse (2) and set of all primes is infinite

Proof of Infinitude of Twin Primes
(1) definition of prime
(2) hypothetical assumption: suppose the set of all primes and twin-
primes is finite with the last two and
largest primes as twin-primes and this sequence list is 2,3, 5, 7,
11, . . , p_n, p_n+2
(3) Multiply the lot and add 1 and subtract 1 yielding W-1 and W+1
(4) both W-1 and W+1 are necessarily new primes and twin primes from
(1) and the fact
that successive division by all the primes that exist in (2) leave a
remainder
(5) now form a new sequence of 2, 3, 5, 7, 11, . . , p_n, p_n+2, W-1, W
+1
(6) Multiply this lot and add and subtract 1 yielding Z-1 and Z+1
(7) continue this recursive multiply the lot and yielding two new
numbers
(8) Contradiction to (2) in that these successive new numbers are
larger than previous and are twin primes by the definition of prime
and the fact that all these new numbers
formed leave a remainder upon division
(9) reverse (2) set of Twin Primes is Infinite

So the question is, are there only two human beings in all the world
who have enough
logic to understand that the above are the only valid Euclid
Infinitude of Primes Indirect Method. There is no other valid Indirect
Euclid procedure because the definition in the first step forces the
Euclid Numbers to be necessarily new primes, because the division
leaves
a remainder. And that the only reason, mathematics never was able to
have a proof of the Twin Primes conjecture, is because mathematics
never had a valid Euclid Indirect until the
1990s.

I refuse to believe that only two human minds are logically good
enough to recognize this
valid proofs. Probably half the mathematicians reading the above
concur that the above is the only valid Euclid Indirect and yielding
the valid Twin Primes infinitude. I think half recognize the above,
but are quiet deer behaving, rather than acknowledge the verity.

I do not expect amateurs like David Tribble to understand or ever
accept the above, because alot of people accept only that which is
published in print and comes from say Harvard or Cambridge logos. Most
people need authority to tell them something is true or not. But I do
expect the managing editor of Mathematical Intelligencer to recognize
the truth of the above.
And I do expect people like Arthur Rubin, even though he hates my guts
to see and accept the above. I do expect Bill Dubuque to see and
accept the above, although he may want to act like a quiet deer in the
forest.

I refuse to believe that humanity which may have approximately 20,000
trained and active mathematicians in the world, I refuse to believe
only two of them-- Karl Heuer and myself
are the only two human minds with enough logic to see the truth of the
above. But then again, knowing human nature, that hatred of someone
who gives the proof of Infinitude of Twin Primes and so easily, by
noting a mistake of others who could not even do a valid Indirect
method, that human nature of hatred and envy, could make 20,000 active
mathematicians
all behave like quiet deer in the forest and ignore all that is said
above.

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: sttscitrans on 21 Jul 2010 04:28
On 21 July, 08:36, Archimedes Plutonium
<plutonium.archime...(a)gmail.com> wrote:

> Hard for me to imagine, or should I say, refuse to imagine that only
> two human beings
> can do a valid Euclid Infinitude of Primes:

>  Karl Heuer gives a correct Euclid IP, indirect method

Heuer never mentions "necessarily" prime.



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