I've claimed the Clay Maths Institute's Millenium Prize re the Reimann Hypothesis
collinskppc at wmconnect.com-T-R-I-M
Fri Jul 16 14:29:04 EST 2004
2004-07-16 [written at "Far Reach"]
To the Clay Mathematics Institute's Reimann Hypothesis Millenium Prize
I, hereby, claim the Clay Institute's Millenium Prize with respect to the
Below, I Prove an arithmetic equivalent of the Reimann Conjecture, and
disclose, completely, the True nature of Reimann's zeta function.
But, first, a personal note. Because of the financial circumstances in which I
was raised, I had to make do without formal training in Mathematics. I am
almost completely self-taught. I ask you folks to understand, therefore, that,
although the methods I will discuss will, at first, seem to Professional
Mathematicians to be "trivial", that circumstance arises solely from the
circumstances in which I learned Mathematics. The methods I will discuss are
exceedingly robust, and in addition to providing resolution to the Reimann
Hypothesis, place all of Number Theory on a new, very solid, very powerful,
foundation. So, please don't dismiss what I share with you folks because it
doesn't look "familiar" to you. If you contact me, I'll send you folks a CDROM
with hundreds of megabytes of easy to comprehend graphical [Geometrical]
demonstrations of the Proof. I can also give you folks a computer program that
implements the Proof in its entirety, allowing an infinite number of
verifications to be performed [and, simultaneously, resolving Maths far beyond
the zeta function. I want to share this computer program, but that needs to be
done in person.]
Thank You for continuing.
1. If the integers are wraped in an outwardly expanding square "spiral", all of
the even squares [4, 16. 36...] fall on one semi-diagonal and all of the odd
squares [9, 25, 49...] fall on the other half of the same diagonal. This is not
complicated. Take a sheet of square-ruled graph paper, leave one central square
unused, start numbering squares, beginning at 1 [2, 3...], at "6:00 o'clock,
moving clockwise around the central open square, to create a square "spiral".
The diagonal extending from the upper-left corner of your square "spiral" to
its lower-right corner will be as above. [The other diagonal, is equally
important, but it's not necessary for the Proof, so I'll let it pass until you
folks work with the computer program.]
1a. The permeating-precision of this square "spiral" discloses the rigorous
order that exists within the set of all integers, which Proves that, even
though they've been deemed to be seemingly-"randomly" distributed, the prime
numbers are also governed by the same all-permeating order -- which is
important be cause it assures us all that the sought-after solution exists.
2. In a way that's reminiscent of the early Proofs of The Calculus, this
square-"spiral" distribution is redrawn, smoothing out the integer-to-integer
angle variations, until a standard spiral, having constantly-decreasing
curvature [constantly-increasing "radius"] is actualized.
2a. The easily-observed "diagonal" distribution of 1., above, seems to
"disappear", but because the constantly-increasing-radius spiral was actualized
via operations that are everywhere-consistent, the all-permeating order is
necessarily preserved, and can, therefore, be rigorously invoked.
3. Taking each integer that is mapped upon this constantly-increasing-radius
spiral, in turn, in order of increasing magnitude, and applying a
rigorously-consistent ruleset that is based on integer mod 2 [3, 5, 6...] = 0,
and adjusting the central angle by a consistent value for each equivalency, the
primes are distributed within the resultant "conjugate-spiral" in
extraordinarily-simple ways -- for instance, all primes fall of one "ray" of
the resultant distribution.
[Sidebar: I converged upon this technique by automating a randomized search
technique. Images of such distributions comprise most of the contents of the
CDROM that I offered, above, to send to the Reviewers. They are
exceedingly-beautiful, and exceedingly-meaningful.]
Because the operations employed are all rigorously-bound, the order inherent in
the original square "spiral" is preserved and carried through. What the process
described does is "raise" the inherent order in a way that's analogous to
literally elevating it in the 3rd dimension "above" the plane of the spiral.
Thus far, all that has been accomplished is establishing a Proven
all-permeating order, and means to operate upon it while preserving it.
Next, this all-permeating order that's been Proven to exist is used as a
"prying instrument" with respect to the prime numbers, with specific recourse
to prime-to-prime intervals [and this next method constitutes a stand-alone
Proof of the Reimann Hupothesis].
4. If the prime-to-prime intervals are accumulated, and these accumulations
graphed over increasing integer ranges [X axis = all the discrete interval
values; Y axis = the counts of each discrete interval value], the result is
that, no matter how many integers are included in each iteration of this
accumulation process, the graph increases in magnitude almost uniformly
throughout it's entire extent.
4a. The above operation is striking. It's literally a proportional-growth
dynamic, and, when viewed in a computer implementation, is almost unbelievably
beautiful. It is so tightly ordered that, when one first looks upon it, one
thinks that one has erred in one's programming. But all that's happening is an
exact arithmetic analog of the Reimann zeta function.
4b. Each of the discrete interval accumulations trades-off being added to in a
way that preserves the overall growth of the entire distribution [of the entire
4c. This trading-off of accumulation-precedence is the fundamental essence of
what is bounded "within" the zeta function, what the zeta function means, and
4d. That is, the rigorous range of the zeta function maps the bounds of the
trading-off of accumulation-precedence amongst the discrete prime-to-prime
interval values, and is a mapping of a fundamental constant within Number
Theory. The computer program that I addressed above, and which I hope to
demonstrate in person, gives this fundamental constant exactly, as a function
of the integers themselves, in a way that is exactly analogous to the way that
the all-permeating order of constantly-increasing-radius spiral was Proven,
above, to be everywhere preserved.
5. This Proof was performed on a relatively low-power stand-alone personal
computer. I have given enough in this Proof of the Reimann hypothesis to enable
anyone to reconstruct [implement] the algorithm within a machine. Anyone who
knows any computer language can recreate it.
Q. E. D.
End note: The essence of the Reimann Hypothesis is extraordinarily-simple, but
that simplicity is what made it seem "hard" to folks who attacked it via
So there was some serendipitous value hidden within my youthful poverty :-]
Sincerely hoping to hear from you folks before too long,
And Sincerely, Period,
K. P. Collins
[Dr.Norman, if you're reading, I Dedicate this work to you, because it was your
challenge that gave me the "heart" to pursue it. Sincere Thanks to you, Sir.
TD E/I(down) to you and yours
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