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June 19th, 2017, 05:25 PM  #11 
Senior Member Joined: May 2016 From: USA Posts: 785 Thanks: 311 
"The string" strongly implies one string. "Infinite number of strings" implies more than one. As I said before, you may have something interesting to say (whether novel or not), but there is no way to tell. You seemed to have started with a cognizable proposition that was interesting, but completely wrong. What exactly are you now proposing for general contemplation, discussion, etc? As far as I can tell, what you are saying is that if a composite number does not have 3 as a factor, it has a larger prime as a factor. I agree wholeheartedly. 
June 21st, 2017, 12:46 PM  #12 
Newbie Joined: Apr 2016 From: Arizona Posts: 10 Thanks: 0 
When I saw this pattern, that shifts when every P^2 entered the equation, I started looking for a graph that would show that the prime aren't random, but that they are controlled by the composites as the pattern changes. Like everyone else I started by leaving in the "interference" of the even numbers. No go. Just pandemonium. I then went to a graph using just the odd numbers from 1 to 49 on the top row. on the second row 51 to 99. I took my graph to seven rows. Then I marked all the "3" composites on the first row and the first one on the second row (51). Starting at the number 3, I dropped to the next row (53), and moved backward to 51. this showed me the pattern for the "3" composites. Going to 15, drop to the next row, back one put it at 63. Also, 15, drop to the next row and forward 2 numbers is 69. The "7" composites worked just as well. 7+508=49. 7+50+6=63. In other words, down one row, back four numbers, or forward three, and the "7" composites are found. There was a pattern for each of the prime/composites on my graph up to 7*49. If the top row is expanded to 1to 99, or higher, the pattern shifts, but it is easy to find. I thought it was interesting, although useless, information, as it isn't useable to detect the very high composites and primes.

June 21st, 2017, 04:37 PM  #13  
Senior Member Joined: Aug 2012 Posts: 1,510 Thanks: 364  Quote:
It's entirely true that the primes are not random in the sense of being undetermined. Martians have the same prime numbers we do. The primes are in some way logically necessary, once we accept the counting numbers and define what we mean by a prime. The distribution of the primes may or may not be statistically random. A lot of people try to understand this problem. There are definitely patterns in the way the primes are sieved. You throw out all the multiples of 2, then of 3, then of 5, and so forth, and of course there must be some clever way to express the resulting pattern. People have been driven by this thought for centuries. A formula that gives the nth prime without having to calculate all the earlier ones. Investigating this subject is a worthy endeavor. I think if you challenged yourself to describe your idea more clearly, people could give more specific constructive advice. Last edited by Maschke; June 21st, 2017 at 04:53 PM.  
June 23rd, 2017, 01:02 PM  #14 
Newbie Joined: Apr 2016 From: Arizona Posts: 10 Thanks: 0 
I only discard the even numbers from my graph. The top row consists of all the odd numbers from 1 through 49. Once the first composite sequence for the prime to composite is found, it holds true for all the other composites of that prime. Ex. 3+48=51, 15+48=63, 21+48=69, and so on up the line. 7+42=49, 21+42=63, etc. Each prime after 5 can be calculated before it reaches P^2, at which point it changes the composite pattern, thus changing the prime pattern. If the top row of the graph is changed to 1through 99, or higher, the pattern for each prime/ composite will shift. 3+102=105, so adding 102 to all the 3 composites will run true on that graph. 7+98= 105. adding 98 to every 7 composite will also run true on that graph. As I said, interesting but useless in the search for the high end primes.


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composites, numbered, odd, question 
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