Adventures In PRIME NUMBER Land !!! ... (A Dummies Guide to Prime Numbers)

reply to post by Deaf Alien

I was analyzing your claim that every prime number squared will always lay on Ray #1. Upon brief analysis, it appear that you are correct.

I am really appreciative of the time you're investing in providing corroborative proof as it makes my claims that much more substantial ... so I'll take all the peer review (good & bad) that you guys want to throw in my direction !

reply to post by PrisonerOfSociety


Yes, I have heard of and seen examples of cymatic generated structures like your examples and have always been struck by their beauty.
I'm in agreement with you that there IS some kind of underlying mathematics that in combination with sound vibrations results in those standing wave patterns.

And I certainly would NOT bet against primes being involved somewhere in the process, either !

Originally posted by Mortimer452
I'm surprised no one has mentioned any possible implications here . . .

As most of our encryption systems are based on prime numbers any increase in the speed of factorisation will render them useless. These methods rely on the computation times required to determine if large numbers are prime or not.

The link I posted on the first page High Speed Prime Test (albeit with a different title!) and subsequent Improvements are the fastest known methods using a Turing Machine to the best of my knowledge. Although the paper may look complex the actual method is quite simple. Have a look at the pseudocode further down.

Research 'Computational Complexity Theory" for more info on how difficult some problems are.

Although I haven't examined the OP properly it appears to be a prime sieve. Sieve of Eratosthenes



[edit on 21/9/2009 by LightFantastic]

By now, you should all be aware of my belief that the entire prime family is dependent on, and revolves around the number 24.

Firstly, take a look at the following table and don't be to concerned about the content at this point, as all will be explained shortly.
For the moment, focus on the column titled "Square root / Prime" and spend a few moments examining it.

This table basically shows how simple it is to generate EVERY odd number sequentially by a simple arithmetical process, which I'll explain shortly.


As should be immediately obvious, this column simply lists all the odd numbers from 1 to 101 sequentially. The two important points to be aware of when looking at this column is (a) the numbers were generated in this sequence by simple arithmetic; and (b) the prime numbers have been highlighted in red


[atsimg]http://files.abovetopsecret.com/images/member/b25baab14729.jpg[/atsimg]

Now, here's how simple arithmetic is used to generate the sequential odd numbers in the final column (Square Root / Prime)

The columns titled "Increment" and "Running total" go hand in hand.

Basically, the "Increment" column starts at 0 and has 8 added to it in each row. So it starts at 0, has 8 added to it to give a total of 8, then has another 8 added to it to give a total of 16, then another 8 added to give a total of 24, and so on all the way down the "Increment" column.

The "Running total" column starts with 1 and has the corresponding "Increment" value for that row added to it. So it starts with 1 and has 0 added to it from the "Increment" column (for that row) giving a running total so far of just 1.
Then we move to the next row and take the "Increment" value of 8 and add it to the previous "Running total" value of 1 to give a new "Running total" value of 9.
Now we move down another row and add the "Increment" value of 16 to the previous "Running total" value of 9, and getting a new "Running total" value of 25.
And so on all the way down the table.


Confused ??? I'll bet you are !
So, how about a picture to make it easier to follow ...


[atsimg]http://files.abovetopsecret.com/images/member/d4ba32e56678.jpg[/atsimg]

Notice that in the "Square root / Prime" column that both 1 and 5 have been highlighted in red to indicate that they are PRIME.


Now take a look at the "Multiple of base 24" column entry.

[atsimg]http://files.abovetopsecret.com/images/member/97af80566965.jpg[/atsimg]
The 8+16=24 entry is there simply to show that a total of 24 (or multiple) has been accumulated by adding the current "Increment" value to previous "Increment" value(s).

The (1x24) entry is there to simply show whether we have a single value of 24 or a multiple value of 24.


[atsimg]http://files.abovetopsecret.com/images/member/e46efc532945.jpg[/atsimg]


[atsimg]http://files.abovetopsecret.com/images/member/ad19345ba203.jpg[/atsimg]



Now the interesting part of all this rambling of mine is to highlight a very curious and interesting feature of this table. Even though this table basically justs generates a (theoretical) infinity of sequential odd numbers, notice that EVERY prime number (Square root / Prime column) has an associated "Multiple of base 24" entry ... again indicating the powerful role played by the value 24 within the entire prime family !

To illustrate this effect, in the following table, I've removed all non-prime rows.

[atsimg]http://files.abovetopsecret.com/images/member/a67e2edc2001.jpg[/atsimg]


I don't know if you're amazed and surprised by this unexpected revelation ... I know I certainly am !

very good stuff

just from my little bit of common sense underdstanding, if you look at the gaps between the prime numbers on your "24"-based system, they are always 1 followed by 3 (one yellow, then a blue prime ray, followed by 3 yellow)

common sense would tell us that you could base your same system on the number "6" instead of "24"

My 2 cents.

The law of the squares. Take a look at it

And the geometry of numbers. Using Phi may help you.

The golden ratio = 1.61803399

Links to start with.

goldennumber.net...

www.searlsolution.com...

Without realizing it you're on your way ---- Free energy - anti gravity

Do not stop

Just an ideia from a crazy guy.

PS: Take a good look at Fibonacci number sequences

en.wikipedia.org...

www.mathacademy.com...





fixed vid

[edit on 21/9/09 by masqua]

reply to post by tauristercus


Why weren't *you* my math teacher in school...?

Very good thread.

Outstanding! S&F with enthusiasm. This is possibly the best thread on ATS ever.

You may find the works of Dr. Peter Plichta interesting...

Apologies but I'm only posting in this thread so that I can come back to it at a later date to read - I'm rather tipsy at the moment y'see. Thank you please.

Edit: k, screw that - curiosity got the better of me; - I'm not gonna pretend that I know anyhting about 'extreme maths' but Prime Numbers have held a kind of interest for me. Sorry to say that I'm gonna have to read this a few time to understand - anyone have a bsic book on Prime Numbers? I'm looking on Amazon/Ebay at the moment.

[edit on 21/9/09 by XHellcatX]

reply to post by tauristercus



Nice thread, there has to be some pattern to primes or something similar to a pattern.

Savants report not seeing prime numbers as numbers but as "patterns or shapes" of a certain "color" when asked how to describe how they can tell if a number is prime or not.

en.wikipedia.org...

reply to post by pavil


Wow, thanks so much for your post! I don't think I have ever heard of synaesthesia until now. I am fascinated. There might be a clue to the whole thing.

Math gurus and mnemonics gurus always teach people to associate numbers and names using imagery. They weren't fooling anyone.

I'm sorry to disappoint you, but your findings will be of little use to number theorists or crypologists.

There's a very simple explanation for why the primes are lined up on special rays like that, and it has to do with modular arithmetic.

24 has 2 prime factors: 2 and 3.

All the non-prime rays contain only multiples of 2 or 3. This is also why 2 and 3 don't fit your pattern. 24 is a nice number because it has lots of little factors, thus the prime lines are going to be consolidated and nice-looking. But you could do the same thing with just about any number. For instance, if we used 20, then the prime lines would be: 1, 3, 7, 9, 11, 13, 17 and 19, also forming a symmetrical pattern. 20 has 2 prime factors, 2 and 5, so all I did was take out all the rays divisible by either of those. In general you would do the same with any modulus number (size of your circle), and unless your circle itself was prime, you'd get some rays with primes and some without.

The idea of using this to get primes has been known for a long time, and although you display it differently, it's really no different than a prime number sieve.

Finding all the squares of primes (except 4 and 9) on line 1 is really cool, something I didn't know, and I salute you for it, but there's a reason for this, too. Modular arithmetic says we only need to check the squares of the first circle. If they all lie on line 1, then all possible prime squares will lie on line 1. Now, all exponents of primes will only lie on prime lines (except exponents of 2 and 3), so we can rule out 16 of the lines already. Of the 5 primes we have to check, their squares happen to lie on line 1. That may seem like a big coincidence, but there's often some interplay between your numbers and your modular base that make it statistically more likely. As an analogy, I once looked at numbers that can be written in two different ways as the sum of two squares. For example, 50 = 1 + 49 = 25 + 25, so 50 is the first such number. It turns out that these numbers are virtually guaranteed to be divisible by 5. This baffled me until i realized it had to do with how the first few squares line up in a mod 5 table.

There's also a good reason, not just convention, why 1 is not a prime like you say it should be. An equivalent way of defining the primes is: "no prime is a multiple of another prime." But this breaks down if we include 1, since every integer is a multiple of 1.

Your equation will not be of use in factoring large numbers. You may have noticed that the equation you use factors into:

p1^2 * (p1^2 + 24n - p2^2) = 0

When you factor it you can see that the roots of the parabola are at p1 because you've defined it that way. But you've just shuffled off the hard work of factoring from yourself to whatever algorithm the graph display program uses. You couldn't use this to factor big (300 digit) primes without taking far more time to display the graph than factoring it a more normal way.

Most number theorists think that the best way toward better understanding primes is through something called the Riemann Zeta Function.
en.wikipedia.org...

S+F.

Good stuff, especially well done on your intro posts they must have taken a lot of effort.

When maths is presented like this I can get really interested in it. Much better than just having it lectured at you.

I'll be following this thread closely.

posting a reply to return

so far so good, i am liking what i am reading.

i look forward to more!

Good work. Arithmetic is fun, contrary to popular belief. Patterns emerge, profound mysteries hide into them.

As has already been said you are correct about the properties of 24, because the properties of 6 are displayed 4 times in the circle.

Obviously only 6n+1 or 6n-1 can be a prime greater than 3, the other values have a factor of 2 or 3.

You are correct about your p² claims.

p = 24*y + x with x < 24
x is either 1, 5, 7, 11, 13, 17, 19 or 23
it can be easily verified that for these values x² mod 24 = 1. This is written simply x² = 1 in modular arithmetic.

Using modular arithmetic, every multiple of 24 is 0, therefore:
p² = 24²*y²+2*24*x*y+x² = x² = 1

The square of the product of 2 primes is 1 too, because
(p1*p2)² = p1²*p2² = 1*1 = 1

Also
p2²-p1² = 1-1 = 0
p²-1=0

Good luck with your experiments!

[edit on 2009-9-21 by nablator]

[edit on 2009-9-21 by nablator]

I believe the ENTIRE prime number system is BASED ON and COMPLETELY revolves around the number 24.

^ BAD

[atsimg]http://files.abovetopsecret.com/images/member/38b08aad7d7a.jpg[/atsimg]

I learned this in my senior year in high school.

(course had set theory, number theory, chaos theory, discrete mathematics, advanced euclidean geometry, modular mathematics,...)

Although I do think this is cooler:

[atsimg]http://files.abovetopsecret.com/images/member/21e6ed9fc39e.gif[/atsimg]



[edit on 9/21/2009 by die_another_day]

reply to post by tauristercus


Good answer - thanks.

reply to post by tauristercus

That's a very nice insight into basic numerical relationships from a non-mathematicians -- it kind of highlights the difference between knowing and understanding. It kind of takes you back to the ancient, starting times when there were no mathematicians by profession but observant folks with an abstract hobby.

A mathematician would be able to explain some of the problems you hinted, but you don't want this kind of interference -- it's better to figure it out with the help of the tools used in ancient times.

I believe that the circle divided into 24 sectors to highlight prime numbers existed long time ago, but the power of modern modular algebra kind of rendered it cumbersome for a practical use, but it should be included in the book that deals with the development and history of this math branch.

People do reinvent things all the time. That's good, coz if you don't know where the cellar is, you may not be able to figure out where the attic is either.
www.geocities.com...
www.geocities.com... Prime Circle

reply to post by Deaf Alien


No problem, find the interviews with Daniel on Youtube, he is not your typical "savant", that's why they call him the Rosetta Stone of the condition, he can actually explain somewhat how he does things. Still pretty amazing.