## Re: [PrimeNumbers] composite number patterns

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• Hey Steve, here is a link to a page I have on composite number patterns: http://www.geocities.com/asposer/composite.html I don t know if it s useful or not,
Message 1 of 3 , Jun 26, 2002
Hey Steve, here is a link to a page I have on composite number patterns:

http://www.geocities.com/asposer/composite.html

I don't know if it's useful or not, but I thought it was interesting nonetheless. I'm thinking of writing a program that will give the degree composition and other fun stuff for a range of numbers. Here's an excerpt from the list:

Composition of the composites:

1st prime: 2
1st 2 degree composite: 2^2
1st 3 degree composite: 2^3
1st 4 degree composite: 2^4
1st 5 degree composite: 2^5

2nd prime: 3
2nd 2 degree composite: 2 * 3
2nd 3 degree composite: 2^2 * 3
2nd 4 degree composite: 2^3 * 3
2nd 5 degree composite: 2^4 * 3

3rd prime: 5
3rd 2 degree composite: 3^2
3rd 3 degree composite: 2 * 3^2
3rd 4 degree composite: 2^2 * 3^2
3rd 5 degree composite: 2^3 * 3^2

4th prime: 7
4th 2 degree composite: 2 * 5
4th 3 degree composite: 2^2 * 5
4th 4 degree composite: 2^3 * 5
4th 5 degree composite: 2^4 * 5

5th prime: 11
5th 2 degree composite: 2 * 7
5th 3 degree composite: 3^3
5th 4 degree composite: 2 * 3^3
5th 5 degree composite: 2^2 * 3^3

That 3^n thing is pretty consistent, i.e. when it shows up in a range (such as the 3rd set and the 5th set), all the numbers above it in that range are 3^k * 2^n, where k is a constant and n increases sequentially (i.e. 2^1, 2^2, 2^3, etc...). Well, for small numbers it is anyway ... :)

-Andrew Plewe-
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