## A new and improved "Sieve of Eretosthenes"?

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• I don t like being told never ,but I have played with primes off and on for years and found no pattern to them. I have recently discovered that there is a
Message 1 of 4 , Feb 3, 2004
I don't like being told "never",but I have played with primes off and
on for years and found no pattern to them. I have recently discovered
that there is a constantly shifting pattern to the primes,themselves,
but there is a constant pattern to the composites. I am "selling" an
idea. If you are "buying", the "cost" is whatever time you expend to
disprove, approve, or otherwise play with it. No copyrite or patent
(pending or otherwise). I have only a basic understanding of algebra,
so please bear with me. I just barely undersand a+b=c. OK. The common
understanding and explenation. All primes, except 2 are odd. Yeah!
That just knocked half the numbers out of the game. Hey!! All numbers
ending in 5 can't be prime. Now my search is down to 12 out of 30
numbers. I think I can cut the search down to 8 out of 30. Let's kick
out the 3's. The way to do that is 3*x+y=possible prime(pp). If x=
(odd), then y=2. If x=(even) then y=1. Thus it starts:
3*1+2=5, prime; 3*2+1=7, prime; 3*3+2=11, prime; 3*4+1=13, prime;
3*5+2=17; prime; 3*6+1=19, prime; 3*7+2=23, prime; 3*8+1=25,
composite, 5*5. That worked prety good up to there, but can I predict
the next composite in the series? Let's see. 5*5+2*5=5*7=35. Carry
on. 3*9+2=29, prime; 3*10+1=31, prime; 3*11+2=35, composite, 5*7.
Ok so far. Now, to compute for the next two composites.
5*7+2*7=7*7=49 and 5*7+4*5=5*11=55. Move it on up. 3*12+1=37, prime;
3*13+2=41, prime; 3*14+1=43, prime; 3*15+2=47, prime; 3*16+1=49,
composite, 7*7; 3*17+2=53, prime; 3*18+1=55, composite,5*11. I
worked this up to 3*333+2=1001, but the floppy was corupted and I
lost all the info. I am working it again on floppy and hard drive for
back up. There are more patterns, but I don't think it will help in
the search for mega primes. Only a small bit of interesting, and
trivial, info.
• http://www.primepuzzles.net/problems/prob_037.htm :) I m currently working on the same idea and over the last year i ve found out several simple properties of
Message 2 of 4 , Feb 3, 2004
http://www.primepuzzles.net/problems/prob_037.htm :)

I'm currently working on the same idea and over the last year i've found out several simple properties of these patterns; currently i'm preparing a written version to give a better tool to enable proves to these and further properties. i'll possibly release it within a month or two.

gerrit begher

[Non-text portions of this message have been removed]
• ... So far, it looks like you re, uh, reinventing the wheel. :) Read this earlier message and see if it s similar to what you re doing:
Message 3 of 4 , Feb 3, 2004
At 01:19 PM 2/3/04 -0000, kenox5252 wrote:
>I don't like being told "never",but I have played with primes off and
>on for years and found no pattern to them. I have recently discovered
>that there is a constantly shifting pattern to the primes,themselves,
>but there is a constant pattern to the composites. I am "selling" an
>idea. If you are "buying", the "cost" is whatever time you expend to
>disprove, approve, or otherwise play with it. No copyrite or patent
>(pending or otherwise). I have only a basic understanding of algebra,
>so please bear with me. I just barely undersand a+b=c. OK. The common
>understanding and explenation. All primes, except 2 are odd. Yeah!
>That just knocked half the numbers out of the game. Hey!! All numbers
>ending in 5 can't be prime. Now my search is down to 12 out of 30
>numbers. I think I can cut the search down to 8 out of 30.

So far, it looks like you're, uh, "reinventing the wheel." :) Read this
earlier message and see if it's similar to what you're doing:

>Let's kick
>out the 3's. The way to do that is 3*x+y=possible prime(pp). If x=
>(odd), then y=2. If x=(even) then y=1. Thus it starts:
>3*1+2=5, prime; 3*2+1=7, prime; 3*3+2=11, prime; 3*4+1=13, prime;
>3*5+2=17; prime; 3*6+1=19, prime; 3*7+2=23, prime; 3*8+1=25,
>composite, 5*5. That worked prety good up to there, but can I predict
>the next composite in the series? Let's see. 5*5+2*5=5*7=35. Carry
>on. 3*9+2=29, prime; 3*10+1=31, prime; 3*11+2=35, composite, 5*7.
>Ok so far. Now, to compute for the next two composites.
>5*7+2*7=7*7=49 and 5*7+4*5=5*11=55. Move it on up. 3*12+1=37, prime;
>3*13+2=41, prime; 3*14+1=43, prime; 3*15+2=47, prime; 3*16+1=49,
>composite, 7*7; 3*17+2=53, prime; 3*18+1=55, composite,5*11. I
>worked this up to 3*333+2=1001, but the floppy was corupted and I
>lost all the info. I am working it again on floppy and hard drive for
>back up. There are more patterns, but I don't think it will help in
>the search for mega primes. Only a small bit of interesting, and
>trivial, info.

---
• Yes. Liu s prime formula is the first formula, which can prove further properties of primes. I wish that you may use the idea to get great success. I try prove
Message 4 of 4 , Feb 4, 2004
Yes. Liu's prime formula is the first formula, which can prove
further properties of primes.
I wish that you may use the idea to get great success.
I try prove the prime k-tuple conjecture, had submited normal
journal, it is very hard to referee it.
Perhaps I will release a now version.
China
Liu Fengsui

>I'm currently working on the same idea and over the last year i've
found out
>several simple properties of these patterns; currently i'm preparing
a written
>version to give a better tool to enable proves to these and further
properties.
>i'll possibly release it within a month or two.

>gerrit begher
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