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Re: [PrimeNumbers] Strengthening Goldbach

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  • mikeoakes2@aol.com
    ... mod 4 No-one has said it has already been conjectured, so I assume it hasn t. Here s some relevant data to back it up. Given a cutoff n, if you total up
    Message 1 of 6 , Jun 2, 2002
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      In a message dated 29/05/02 08:35:16 GMT Daylight Time, I wrote:
      > every integer = 2 mod 4 can be expressed as the sum of 2 primes each = 3
      mod 4

      No-one has said it has already been conjectured, so I assume it hasn't.
      Here's some relevant data to back it up.
      Given a cutoff n, if you total up the number of ways each of the integers
      less than n which are = 2 mod 4 can be expressed as the sum of 2 primes each
      = 1 mod 4 (total1), and do the same for = 3 mod 4 (total3), you get the
      following:-

      n total1 total3 total3/total1
      10 5 3 0.6
      100 105 107 1.01904762
      1000 4045 4344 1.07391842
      10000 209824 217155 1.03493881
      100000 12602761 12773813 1.01357258
      1000000 834142745 837815535 1.00440307

      So the stronger conjecture, that the ratio => 1 as n => infinity, seems
      eminently reasonable.

      Anyone for a proof? (only joking...)

      Mike


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