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  • kadhirvel
    for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and their prime factor either 3 or 5 or 3 and 5.And the converse is not true. Send instant
    Message 1 of 3 , May 31 8:18 AM
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      for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and their prime factor either 3 or 5 or 3 and 5.And the converse is not true.

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    • kadickv
      for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and their prime factor either 3 or 5 or 3 and 5.And the converse is not true.
      Message 2 of 3 , May 31 8:28 AM
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        for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and
        their prime factor either 3 or 5 or 3 and 5.And the converse is not
        true.
      • Jens Kruse Andersen
        ... 3 always divides one of N, N+2, N+4. By gap = 3 I assume you mean that N and N+4 are consecutive primes. Then 3 must divide N+2. And then 3 divides
        Message 3 of 3 , May 31 10:52 AM
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          kadickv wrote:
          > for prime(N) if gap = 3 then both 2N + 1 and 2N + 7 are composite and
          > their prime factor either 3 or 5 or 3 and 5.

          3 always divides one of N, N+2, N+4.
          By "gap = 3" I assume you mean that N and N+4 are consecutive primes.
          Then 3 must divide N+2. And then 3 divides 2*(N+2) = 2N+4.
          This means 3 also divides 2N+1 and 2N+7.

          We know that 5 doesn't divide 2N or 2*(N+4) = 2N+8.
          Then 5 must divide exactly one of 2N+1, 2N+4, 2N+7.

          --
          Jens Kruse Andersen
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