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Re: [PrimeNumbers] Important prime number relationship

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  • Phil Carmody
    ... Pb+Pa is not the difference between Pa and Pb. ... Ditto. ... Care to disambiguate what you really mean before we invest effort in the wrong one. Did you
    Message 1 of 4 , Apr 9, 2006
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      --- jcmtnez90 <jcmtnez90@...> wrote:
      > Looking at prime number you can see this relationship:
      >
      > Conjeture:
      >
      > "Any prime number can be written as the product of two primes plus or
      > minus the difference between them."
      >
      > This means that at one(at least one) or more of these four
      > relationships must be hold for every prime number:
      >
      > (Pb*Pa)+(Pb+Pa)

      Pb+Pa is not the difference between Pa and Pb.

      > (Pb*Pa)+(Pb-Pa)
      > (Pb*Pa)-(Pb+Pa)

      Ditto.

      > (Pb*Pa)-(Pb-Pa)
      >
      > Pb>Pa And both primes,(To Be consecutive primes is not a requierement)

      Care to disambiguate what you really mean before we invest effort in the wrong
      one. Did you actually mean "plus or minus the sum of, or difference between,
      them"

      I don't know if you've noticed that
      Pa*Pb+Pa+Pb = (Pa+1)*(Pb+1)-1
      and similar expressions for +-, -+, --.
      So you can check your conjecture by looking at product of numbers which are
      primes+/-1.

      Phil
      P


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    • Mark Underwood
      ... Putting aside that there is no solution for the prime 2, the first few cases where it does not hold are p = 101, 173 and 367. (Nice try though!) Mark
      Message 2 of 4 , Apr 9, 2006
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        --- In primenumbers@yahoogroups.com, "jcmtnez90" <jcmtnez90@...> wrote:
        >
        >
        > This means that at one(at least one) or more of these four
        > relationships must be hold for every prime number:
        >
        > (Pb*Pa)+(Pb+Pa)
        > (Pb*Pa)+(Pb-Pa)
        > (Pb*Pa)-(Pb+Pa)
        > (Pb*Pa)-(Pb-Pa)
        >

        Putting aside that there is no solution for the prime 2, the first few
        cases where it does not hold are p = 101, 173 and 367. (Nice try
        though!)

        Mark
      • jcmtnez90
        You are right, therefore I will change the conjecture to every prime greater than 2.
        Message 3 of 4 , Apr 9, 2006
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          You are right, therefore I will change the conjecture to every prime
          greater than 2.
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