rename it as Guiding-Proofs-Validation Nursing-theorem to theInfinitude of Twin Primes proof; proof of infinitude of irrationals

**a_plutonium** · #1 March 6th 06 posted to sci.math,sci.logic,sci.physics

wrote:
--- quoting from a post of mine a few days ago ---
Here is a proof of the Infinitude of Twin and all
even-numbered-Metric-primes

for twin primes construct ((2x3x5x...xP)+1 and ((2x3x5x...xP)-1
Construct ((3x5x....xP)+2 and ((3x5x....xP)-2 for quad-primes
Construct ((2x5x7x....xP)+3 and ((2x5x7x....xP)-3 for hex-primes
Construct ((2x3x7x11x....xP)+5 and ((2x3x7x11x....xP)-5 for deca-primes
Construct for the general case of even number metric prime

Notice that in some even numbered metric that a prime is deleted as the
case of 2 in quad primes or 3 in hex primes.

Proof (for twin primes and all the others follow in the same manner):
Suppose false then there is a last and final prime of a twin prime pair
call it P. Construct ((2x3x5x...xP)+1 and ((2x3x5x...xP)-1. Those two
are necessarily primes and they are twin primes and larger than the
twin
prime pair which had P. Contradiction, and hence infinitude of Twin
Primes.

What makes it such an easy proof is that the Indirect method guarantees
the constructed new numbers are prime. It guarantees that fact because
those were all the primes in existence in the supposition.

The reason no-one between Euclid and Archimedes Plutonium proved Twin
Primes is that no-one saw the inherent logic of a valid Indirect proof
of Infinitude of Primes.

However, what is puzzling is that the valid direct method proof of
Infinitude of Primes is unable to deliver a proof of Infinitude of Twin
Primes for the reason being that the regular primes are mixed in with
the even-numbered-metric primes. In the Indirect Method because the
regular primes are mixed in with the Twin primes is the reason we can
fetch a proof, but in the direct method we cannot fetch a proof for we
are not guaranteed that both ((2x3x5x...xP)+1 and ((2x3x5x...xP)-1 are
prime.

So here is an example in mathematics where a Indirect Method proof
exists but a Direct Method cannot exist (at least I cannot see a bridge
at this moment). And if that is true, then my conjecture of the
asymmetry between Direct and Indirect is true. Infinitude of Primes has
both Direct and Indirect proofs but Twin Primes has only a Indirect
proof. And law of excluded middle does not seem to enter into why Twin
Primes has only a indirect method proof.
--- end quoting ---

The concept of a Nursing-theorem is a excellent concept for it is a
better judge of whether a new proof is valid or not. For example the
Appel&Haken and the R,S,S,T have no nursing theorems and thus are not
proofs but models. Another example is Wiles's alleged FLT has no
nursing theorem and his is not a proof.

The Kepler Packing and 4 Color Mapping are nursing-theorems where both
are so much alike that one guides the other.

If in mathematics a theorem has no nursing theorem, indicates it is
likely to be a fake. This is probability not certainty.

So the above is my proof of the Infinitude of Twin Primes and all
even-numbered-Metric-Primes. Is it valid? Well the best test for
validity is not the old way of testing where you send it off to some
math journal and have a group of so called experts judge it for they
invariably have their own selfish interests involved to denounce it or
if paid for it to place on a pedestal even though they know it is
flawed. So there is too much human error and human judgement. That is
one of the reasons Physics is king and math a tiny subdepartment of
physics because the judge of physics is not some group of men with
their folly of judgement but is Experiment that judges physics.

So I propose a better judge of a math proof validity. Can you provide a
Nursing Theorem. Another theorem old in record and which has similar
aspects as the new sought for theorem. Keep in mind that KPP had no
proof until I proved it circa 1991-1993. And the 4CM theorem of Appel
and Haken was not widely accepted. But I put the two together as
Nursing Theorems here on the Internet in 2006, where one guides and
leads the other.

Now I claim the Twin Primes Infinitude proof above and is there a
Nursing-Theorem for that above Twin Primes proof. Is there an olden
proof that matches the Twin Primes argument.

I believe it is the proof of the infinitude of Irrational Numbers,
algebraic and the transcendental. Notice that in the irrational numbers
proof that a reductio ad absurdum seems necessary. And notice that in
my Twin Primes proof that reductio ad absurdum seems necessary.

It is actually a method for which we mostly dispense with a crowd of old
men in back rooms deciding on whether a manuscript for a math proof
offering is acceptable for print publication. What the method does is
validate or invalidate when someone thinks they have a proof.

The way it works is that anyone claiming to have a proof of say Kepler
Packing must accommodate and place in tandem with another proof in
mathematics that is already accepted. The reason why this works so great
is because these two tandem proofs have very similar Symbolic Logic
underpinnings and one proof guides the other proof.

Now I gave a proof offering of Infinitude of Twin Primes way back circa
1993 to professors at Notre Dame University and they rejected my
offering, noting that it had "symmetry" for which I was grateful of
their note. But what I should have done is not submitted it in isolation
but have submitted it with a already established proof of another
theorem for which the Symbolic Logic underpinnings matched Infinitude of
Twin Primes. I suspect but not explored in detail that the infinitude of
irrationals, algebraic and transcendental, is such a
guiding-proof-validator. But I am looking to geometry to find a guiding
proof validator.

The reason this method is a great new thing is that it dispenses with
having alot of old men in mathematics to come together to decide if
someone's treatise is valid or invalid. Where the accompanying GUIDING
PROOF of a different theorem does most of the work. Does most of the
judge and jurying and refereeing.

You see, that is why Physics is the King and mathematics is the closet
attic space inside of physics, because physics has the ultimate judge
and jury and referree--- EXPERIMENT, whereas mathematics constantly has
to go to physics for its ultimate truth validation.

Archimedes Plutonium
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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