vectors and prime numbers

[AntonioLao]

vectors are like prime numbers, which cannot be divided by any number except by one and itself.

What is the largest prime? What is the largest vector? What is the longest and straightest line? Is it infinity? Can the straightest line be the shortest line? To give a satisfactory answer to any of these questions is to prove the correctness of the Riemann Hypothesis, the greatest remaining unsolved math problem since Fermat's Last Theorem, which was proven by Andrew Wiles in 1995.

[mkirkpatrick]

The straightest line between two points is only the shortest when in realitivity.
in the absolute sense there is no line and no point,and of course there is no distance,as that cannot exist in absolute being.The only real number is one there is no two or three or four hundred and twenty six,just One,Now in the realitive sense we have many numbers,to entertain our selves with,it gives us
satisfaction to find the square root of an oxo-cube!to add up great stacks of letters and numbers,and then find a solution to all that hard work!All these things have a place,and rightly so,but so does the other side of the equation,
When you focus on matter or force,or light,they are all the same,the more you look within,the more focussed you become the many so called differing things
begin to meld-into one-is that not so!So the only real number is One and within
that one mind we all live and move and have our being.


kind regards michael.

[Guille]

Antonio,

There is no a highest prime or vector. There are infinite of them. They can be infinatelly big. This is a problem. It is derived from the same thing as zeno's paradox. If space can be infinatelly devided, it has infinte longitude. Just like fractals. What's the distance from my head to the screen? According to Mandelbrot, it is infinite infinites.

[AntonioLao]

The object of this post is to make an assertion that vectors (similar to prime numbers) cannot be divided except by itself and by one. In fact, it cannot be divided by itself if we conform to the strict rules of division.

[Cubola Zaruka]

Vectors can be divided, but there are 2 ways of multiplying them, so there are also 2 ways of dividing them (dot and cross). The shortest line is alway the straightest. If there were a largest prime, a larger prime could be created by multiplying together all the primes up to that number and subtracting 1, so there must be an infinite number of primes.

[SteveA]

vectors are like prime numbers, which cannot be divided by any number except by one and itself.

What is the largest prime? What is the largest vector? What is the longest and straightest line? Is it infinity? Can the straightest line be the shortest line? To give a satisfactory answer to any of these questions is to prove the correctness of the Riemann Hypothesis, the greatest remaining unsolved math problem since Fermat's Last Theorem, which was proven by Andrew Wiles in 1995.

I don't believe the Riemann Hypothesis is actually provable using a system of real numbers, though it may be provable using discrete representations.

I say this because there are multiple infinite quantities involved in the construction of the complex zeroes in the Riemann zeta function and multiple independent limits involved. The relative magnitudes of these various infinite quantities is unspecified and arbitrary though there are typical assumptions most mathematicians make regarding their interplay that could make a proof using real numbers appear to be rigorous, yet ultimately, the generally anticipated "deep insights" of such a proof would not be present and we could instead have nothing more than, yet another, glossy layer of obfuscation.

Notice that mathematical "proofs" based upon physical analogy cannot be guaranteed accurate on all orders of infinitesimal detail. For example, if we rotate a protractor on a piece of paper and assume a uniform circumference for a circle can be drawn, there are multiple potential flaws to this assumption:

1) Were all points on infinitesimal scales traversed?
2) Do the start and end points of this circle overlap and if so, does the double use of a single point in the circumference cause an asymmetry? If the start and ending points are not coincident, then how is the cycle completed and assured a connection to the initial point?
3) A physical passage of time during the rotation alters the distance between these points temporally and where the beginning would not be where the end results at least temporally (but I believe there's more to this as well).

As a good mathematical example of the problem, let's construction a complex version of the base of the natural logarithm:

e(complex)=lim((1+i/n)^n) as n->infinity

This converges to a point on the complex plane that appears to be at a unit distance from the origin and rotated by a single radian from the real axis.

Now let's write another version of this that would also be considered equal:

e(complex)=lim((1+i/n+i/n^2)^n) as n->infinity

Notice that n^2 grows much faster than n, n^2 >> n and that the reciprocal influence of i/n^2 is infinitesimal relative to i/n.

Though both equations appear to approach the same constant (ir)rational bound, e(complex), are they mathematically identical? Without adding anything to this, the assumption of, at most, negligeable infinitesimal differences appears justified (physical construction representing each could be make indistinguishable), but consider if we truly viewed these two processes as giving logically identical results and we desired to work with both versions in a single equation:

If we used both of these vectors as units of exponential rotation, and integrated them over n^2 units of rotation, the results would diverge into non-infinitesimal differences, and without becoming overly detailed, one form would be integrated over roughly n^2 radians, whereas the other would be integrated over an additional radian and be offset.

This may seem a somewhat contrived example, but this directly applies to a very large subset of modern mathematics based upon Euler's Identity, which is actually just a definition of an assumption based upon physical reasoning applied to physical analogies of ideal circles (which contain logical paradoxes and are even mathematically unconstructable - for example, the idea of a circle representing an infinite number of cycles is paradoxical in that the circumference already contains an infinite number of points, so traversing the circumference already requires an infinite and unterminated sequence be constructed, and there would be no manner to complete a single cycle around a cycle in order to begin repeatitions of such an infinite number ... you're only going to be able to begin completion of one largest infinite and any other "infinities" are subsets of this).

Anyway, I recognize I'm not detailing this now as much as some may desire, but the initial reason why I posted was that once you break things up into discrete units, the prime numbers pop up rather easily and it appears likely to me that potentially all problems can be mapped to computing interactions between various wavelengths of motion in a "vortex-like" structure with a single (central) intersection point for each of these pathways performing the computations for the system.

The most obvious initial feature that this structure appears to naturally exhibit (especially on large scales) are "spectrums" of wavelengths exchanging information based upon the relative primality between each. For example, a pathway with a delay of 3 units of time and another pathway with a delay of 5 units of time will not synchronize and will appear to interact randomly/uniformly across their co-constructed "volume" of time (3*5/gcd(3,5)= 15 units), whereas information travelling in two pathways with delays of 4 and 6, for example, would share a common binary synchronization in phase (2*2=4, 2*3=6) and appear as two independent objects with identical "volumes" of time (4*6/gcd(4,6)=24/2=12 total units of time per cycle or 6 units of time for each of 2 independently phased objects).

It appears that there are ways of showing that such structures should inevitably exist as a foundation of conscious perception if we make a few assumptions that there exist discrete perceptions over time and at least the equivalent of memory of past events with predictive abilities made from these.

Ok, I ramble some, but I enjoy the subject of prime numbers (or generally, the equivalent irreducible properties in any field), though again, I'm skeptical that a proof of the Riemann Hypothesis would actually be rigorous and especially useful, unless it was based upon an equivalent discrete derivation showing a proof of the expected characteristics.

[AntonioLao]

Regarding the location of prime numbers on the real line, I am using a sieve of Diophantus to describe the provable location of twin primes as well as all the locations of infinite number of primes. I hope to publish this idea and at the same opportunity give an algorithmic proof of Goldbach conjecture.

[G_burnett]

Regarding the location of prime numbers on the real line, I am using a sieve of Diophantus to describe the provable location of twin primes as well as all the locations of infinite number of primes. I hope to publish this idea and at the same opportunity give an algorithmic proof of Goldbach conjecture.

that was the million dollar prize winner need to that string of binary i gave... let me know when you have it g

[AntonioLao]

This is analogous to the chicken or the egg comes first, the proof or the million dollars. It takes millions of second of time to provide the proof and seconds are humanly equivalent to dollars.

[G_burnett]

....with no zero and first 1 removed to counter no zero point singularity IMHO we have the binary for prime numbers represented in the string. ... point is what can be calculated to come next ... it is the million dollar question in hard cash offered. enjoy g