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## Primes and Composites

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• I have taken time in to write something worthy of your valuable time.   Nothing really new, just my attempt at understanding the relationship between
Message 1 of 4 , Aug 11, 2008
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I have taken time in to write something worthy of your valuable time.

Nothing really new, just my attempt at understanding the relationship between composite numbers and prime numbers.

First of all all natural numbers greater than 1, are eitheir prime or composite, never both. As such to study the other, you use the other. Meaning if you want to see if there is a pattern in prime numbers, it follows that you will use composites. Also if you want to study primes, you would then use composites. The Goldbach Conjecture is an example which uses primes to relate primes to composites.

I have for sometime now, been struggling with expressing all composite numbers based on prime numbers. In short, I have been trying to establish a pattern in primes using only composites.

I have observed the following:

Intervals in composite numbers are determined by the squares of primes. The meaning of this is that, the first composite [4] is a square of the first prime [2]. All the composites that follow next are even numbers [f(x) = 2x], until the square of the next prime [9]. After [9], the next composites will only be multiples of 2 and 3 ONLY [f(x) = 2x,3x] until [25]. After [25], the next composites will be f(x) = 2x, 3x, 5x, until [49] and so on.

The pattern of how composite progress in relation to primes is as shown below:

(p1)^2,
[f(x) = (p1)*x],
(p2)^2,
[f(x) = (p1)*x, (p2)*x],
(p3)^2,
[f(x) = (p1)*x, (p2)*x, (p3)*x],
(p4)^2,
[f(x) = (p1)*x, (p2)*x, (p3)*x, (p4)*x],
:
:
:
(pn)^2,
[f(x) = (p1)*x, (p2)*x, (p3)*x, (p4)*x, ... , (pn)*x],
:

So far this is what I can share with you for now without wasting anymore of your time. If you dont mine, please share your thoughts.

Thanks.

Billy.

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• ... Perhaps I do not understand the question, but the primes are trivially *not* arithmetic. They do however contain arithmetic progressions of all lengths,
Message 2 of 4 , Aug 11, 2008
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> Does Eric Rowland's formula not also=9Ainfer (prove?)=9Athat
> the prime numb= er sequence =0A3,5,7,11 ... is incidentally
> an arithmetic progression, even= though we cannot pinpoint
> precisely what the arithmetic progression is?=0A=

Perhaps I do not understand the question, but the primes are trivially *not* arithmetic. They do however contain arithmetic progressions of all lengths, but tat follows from Green and Tao, not Rowland.
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