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773RE: [PrimeNumbers] New Conjecture on Twin Primes (stronger than Goldbach's)...

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  • Jon Perry
    Apr 7 10:08 AM
      WHat's so great about part 3:

      (1.3) The members of E are all the sums of some prime numbers.

      If you look at:


      you will find:

      It has been proven that every even integer is the sum of at most six primes
      [Ramaré95](Goldbach suggests two) and in 1966 Chen proved every sufficiently
      large even integers is the sum of a prime plus a number with no more than
      two prime factors (a P2). In 1993

      Any estimation on the size of E?

      Jon Perry
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      -----Original Message-----
      From: Gert Bohn [mailto:gbohn@...]
      Sent: 07 April 2001 11:20
      To: Primenumbers Forum
      Subject: [PrimeNumbers] New Conjecture on Twin Primes (stronger than

      Hello to each of the primenumbers community !

      ... and it is also stronger than "There are infinitely many prime twins".

      This mail list does not allow attached files, so i will only cite from the
      paper's abstract.

      The complete paper (electronic, 55KB, five pages to print)

      can be obtained from me via email to gbohn@....

      ( Dick Boland, i sent it to you already, so this is not new to you )



      From the abstract:

      Christian Goldbach's conjecture that every even number is the sum of some
      prime numbers

      gave rise to the question what would be the matter if we replaced "prime
      numbers" by

      "prime twins" i.e. such prime numbers p where p + 2 or p - 2 is also prime.

      The question was looked at by computer programmes, and ...

      ...the following conjectures resulted:

      (1.1) Only a finite set E of even numbers are NOT the sum of prime twins.

      (1.2) The members of E are all the differences of some prime twins.

      (1.3) The members of E are all the sums of some prime numbers.

      [Non-text portions of this message have been removed]

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