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A new and improved "Sieve of Eretosthenes"?

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  • kenox5252
    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
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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 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.
    • Gerrit Begher
      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
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        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]
      • Ben Bradley
        ... 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
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          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:

          http://groups.yahoo.com/group/primenumbers/message/10491

          >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://mindspring.com/~benbradley
        • liufengsui
          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
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            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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