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Re: [PrimeNumbers] Kaveh's question

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  • Ronny Edler
    Hi! Maybe Kaveh could use a Monte Carlo-type test - i.e. pick a fixed number of randomly chosen k s to test and look whether the respective difference exists.
    Message 1 of 4 , Nov 12, 2006
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      Hi!

      Maybe Kaveh could use a Monte Carlo-type test - i.e. pick a fixed number of
      randomly chosen k's to test and look
      whether the respective difference exists. This can be done in O( min(m,n) *
      iterationCount)
      [assuming you can check in O(1) whether a given number belongs to a set].

      Furthermore if there are at least two solutions to a given k, return false.

      Another simple tests that may speed up the process is to check first whether
      min_element(A) < max_element(B)
      If this holds return false, since one can construct a negative number thus
      missing at least one number from [0,mn-1].
      Runtime: O(max(m,n))

      I have constructed some covering sets - there aren't that many (if you bound
      the members of the set to be in [0,mn-1]!).
      So unless explicitly constructed it is very unlikely that two sets have the
      desired property
      [exponentially small in the number of iterations - if you choose each set
      member uniformly at random].

      HTH,
      Ronny
    • Billy Hamathi
      Hi, I am new to this group, and I have been doing some work on prime numbers that I feel I should share with others interested in prime numbers. I have
      Message 2 of 4 , Nov 13, 2006
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        Hi,

        I am new to this group, and I have been doing some
        work on prime numbers that I feel I should share with
        others interested in prime numbers.

        I have attached a document that supports my claim,
        please comment on my paper after reading it.

        Thanks,

        Billy Hamathi.



        ___________________________________________________________
        The all-new Yahoo! Mail goes wherever you go - free your email address from your Internet provider. http://uk.docs.yahoo.com/nowyoucan.html

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      • Ronny Edler
        ... Actually there are _exactly_ 0% prime numbers in the naturals... There are about x/log(x) prime numbers less than x - see:
        Message 3 of 4 , Nov 14, 2006
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          >There are approxiametly 29 % prime numbers in the positive integers range

          Actually there are _exactly_ 0% prime numbers in the naturals...

          There are about x/log(x) prime numbers less than x - see:
          http://primes.utm.edu/howmany.shtml

          Now the ratio primes/naturals = (x/log(x)) / x = 1/log(x) which converges to
          0 as x approaches infinity.


          Ronny
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