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Originally posted by mathfreak
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.
Originally posted by stander
If the elimination of non-prime numbers the way it was presented in its essence cannot find primes, would you be able to demonstrate the method which does the job in its numerical, not abstract/generalized form?
The OP mentioned all the arguments that you presented and concluded with prime factorization, the applicable part of primes. He just used a long lemma to get there as an intro for those who are not overly familiar with the subject.
[edit on 9/22/2009 by stander]
Originally posted by ALLis0NE
reply to post by bsbray11
Well from what I have read from other very knowledgeable people, and from what I concluded on my own, in the center of everything is GOD, not "nothing"
originally posted by: tauristercus
Continued from previous post ...
Ok, the 1st thing I need to state and absolutely crucial to everything that subsequently follows in this thread, is that
I believe the ENTIRE prime number system is BASED ON and COMPLETELY revolves around the number 24.
As they say, a picture is worth a thousand words.
To illustrate my statement above, lets create a number of concentric circles and divide each of them up into 24 segments. You can picture the 1st circle as a clock with 24 hours ... starting from 1 and going around to 24.
The next outer circle can be pictured as a clock starting at 25 and going around for another 24 segments to finish at 48.
The third outer circle can be pictured as a clock starting at 49 and going around for another 24 segments to finish at 72.
So what we end up with is an infinite number of concentric circles, each divided up into 24 segments:
Circle 1 ---> 24 segments labeled 1 to 24
Circle 2 ---> 24 segments labeled 25 to 48
Circle 3 ---> 24 segments labeled 49 to 72
Circle 4 ---> 24 segments labeled 73 to 96
and so on for infinity.
Notice that starting position 25 (on circle 2), is directly above starting position 1 (on circle 1) ... and that starting position 49 (on circle 3) is directly above starting position 25 (on circle 2), etc
Much easier to show then to explain !
So, in the above diagram, what I've essentially done is started counting numbers starting from 1 all the way to number 24, and put these numbers on the 1st circle ... I've then continued counting for another 24 numbers (i.e. numbers 25 to 48) and put them on circle 2 ... I've then continued counting for another 24 numbers (i.e. numbers 49 to 72) and put them on circle 3 ... and so on.
The diagram itself is very intuitive, allowing students to see how numbers all work together based on a spiral with 12 positions. 12, or 12x (multiples of 12) is the most highly composite system, which is why we have 12 months in a year, 12 inches in a foot, 24 hours in a day, etc. 12 can be divided by 2, 3, 4, and 6. So can all multiples of 12. For every 12 numbers there is a chance of 4 numbers being prime. They happen to fall in positions (think clock positions) 5, 7, 11, and 1.
...It turns out that when the device is examined, the digital roots of the numbers in positions 3, 6, 9, and 12 constantly repeat the same sequence 3, 6, 9!