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Re: [PrimeNumbers] Re: What would be the strongest form of "Mills' constant"?

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  • Phil Carmody
    ... Far from it. But Mills constant purely exists because of the proved nature of the existence claim. Hunting for a progression that works, but is
    Message 1 of 49 , Mar 16, 2012
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      --- On Sat, 3/17/12, WarrenS <warren.wds@...> wrote:
      > --- In primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...> wrote:
      > > --- On Fri, 3/16/12, WarrenS <warren.wds@...> wrote:
      > > > > http://primes.utm.edu/top20/page.php?id=27
      > > > I believe
      > > > In fact, I believe
      > > > Some might even go further and conjecture
      > > > Apparently
      > > > Specifically, I would conjecture
      > > > And one might even conjecture
      > > > Now I think it ought to be
      > >
      > > You've kinda missed the point.
      >
      > --Apparently Phil objects to anything that is conjectured
      > rather than fully proven.

      Far from it. But Mills' constant purely exists because of the proved nature of the existence claim. Hunting for a progression that works, but is unprovable, is hunting for an entirely different beast. There could exist a RH-dependent equivalent, of course, but even then, that's a million miles from something that is merely not known to fail yet.

      > In particular, Phil enjoys programming computer searches for
      > primes.

      Welcome to the early-mid 2000s, enjoy your stay.

      > Again, I ask: which is more important: this sacrifice in
      > ideological purity, or 99.9999999%
      > of the usefulness?

      Well, if we're in the context of proven things, then I'd like to keep "proof" as an absolutely essential component. Anything else is a different beast.

      Phil
    • kadhirvel
      Hi, I had a methodology(may be not efficient had a intuition it will be useful) to generate all odd composite. Factors of all odd composites are predetermined
      Message 49 of 49 , May 7, 2012
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        Hi,
        I had a methodology(may be not efficient had a intuition it will be useful) to generate all odd composite. Factors of all odd composites are predetermined through multiples of 4. Let A(n) = 4n where n = 1,2,3... Then A(n) = P1Q1 = P2Q2 = ..... = PkQk be the 'K' possible set of distinct even factors(means both Pk,Qk  should even) such that Pk > Pk-1 > Pk-2 > ....> P1 then  (Pk  + 1) (Qk  + 1),   (Pk-1 + 1)(Qk-1  + 1), ......   (P1 + 1)(Q 1  + 1)    will eventually generate all odd composite numbers. For e.g. A(1) = 4 = 2x2 here P1 = 2, Q1  = 2. Then (P1 + 1)(Q 1  + 1) = (2 + 1)(2 +1) = 9 First odd composite. A(2) = 8 = 2x4 here P1 = 2, Q1  = 4. Then (P1 + 1)(Q 1  + 1) = (2 + 1)(4 +1) = 15 second odd composite A(3) = 12 = 2x6 => 3x7 = 21  third odd composite A(4) = 16 = 2x8 = 4x4 => 5x5 =25 fourth odd composite and 3x9 = 27 fifth odd composite like that it continues. Based on this i found a methodology to
        sieve Primes in given range 'a' to 'b' a,b both odd numbers. Write all the odd composite between 'a' to 'b' Find 'm' even such that 3(m + 1) <= 'a' < 3(u + 3) Now v= u/2 Calculate 4v = P1Q1 = P2Q2 = ..... = PkQk Then omit the following numbers  (Pk  + 1) (Q k  + 1),   (Pk-1 + 1)(Q k-1  + 1), ......    (P1 + 1)(Q 1  + 1)  which falls in the range 'a' to 'b' Now increment 'k' and repeat the procedure till (Pk  + 1) (Q k  + 1) > b. Now the remaining numbers are prime. 

        With regards
        yourskadhir@...

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