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Now given Natural Numbers = Infinite Integers (adics), I do not know
why it is so easy for the subject of mathematics to have started in
Ancient Greek times and for there to be such an easy proof of the
Infinitude of Regular Primes. Why Regular Primes would have an easy
Direct Method and easy Indirect Method, and yet every other class of
primes such as Twin Primes, 4-primes, 6-primes, etc etc would be
impossible to prove under the failed system of Finite Integers.
This is all well and good because the formation of the Adics in p-adics
relies on prime number concept itself. So this is a bit of a mystery
which my mind is still wrestling with. As to how mathematics could have
even begun in Ancient Greek when the Natural Numbers would be found
several milleniums later as really the Infinite Integers.
But I can offer a good guess as to why Twin Primes could never be
proved in the old Finite Integers. And the same answer holds for
Riemann Hypothesis. The answer is that the old Finite Integers (which I
call the delusional set or mirage set) were thought of as numbers
forming a straight line or on a straight line. Like in the Riemann
Hypothesis the primes and Finite Integers would lie on the 1/2 Real
Line.
So here is the answer from Natural Numbers = Infinite Integers, and
that these begin to curve and do not form a straight line. So we have
to readjust to what we think of as a metric of distance of 2 apart. You
see we think that 5 is a distance of 2 away from 7. That is fine and
dandy if all these numbers are on a straight line in that a concept of
distance 2 makes sense. But if a line curves, then the concept of Twin
Prime really no longer makes any sense. Even though we can visualize
the Infinite Integers of ....999995 and .....9999997 as a metric
distance of 2 apart and thus satisfying our old and trite feelings that
these are Twin Primes or that on the other side of this huge curve of
Natural Numbers that the Twin primes of 29 and 31 are a metric distance
of 2 units apart.
But when all the Natural Numbers form a huge spirally curve, then the
concept of Twin primes falls apart because a distance of 2 no longer
makes sense on this huge curve.
So that is my crude explanation at this moment as to why Ancient Greeks
found a proof for Infinitude of Regular Primes yet no-one in the past
milleniums could touch Infinitude of Twin Primes.
And also, supporting evidence comes from the fact that the Riemann
Hypothesis in old system of Finite Integers is impossible to prove, not
just because these numbers lie on a curve and not a straight line but
also because of the Non existence of a Negative numbers Riemann
Hypothesis. You see, the old Finite Integers would have a symmetrical
look alike of a Negative Number Riemann Hypothesis, but it does not.
And the reason it does not is because the Natural Numbers are the
Infinite Integers and they spiral back around.
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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