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Re: [PrimeNumbers] Union of 2 Sets of Primes in Arithmetical Progression

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  • Jens Kruse Andersen
    A (CP-N), N =4, is N consecutive primes with gaps alternating between two different values. The first (CP-8) has gaps 10 and 8:
    Message 1 of 4 , Feb 4 10:12 AM
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      A (CP-N), N>=4, is N consecutive primes with gaps alternating between two
      different values.

      The first (CP-8) has gaps 10 and 8:
      67944073,67944083,67944091,67944101,67944109,67944119,67944127,67944137

      The first (CP-9) has gaps 2 and 28 (sum 5#):
      1860017189,1860017191,1860017219,1860017221,1860017249,
      1860017251,1860017279,1860017281,1860017309

      The first (CP-10) has gaps 16 and 14 (sum 5#):
      5373097559,5373097573,5373097589,5373097603,5373097619,
      5373097633,5373097649,5373097663,5373097679,5373097693

      --
      Jens Kruse Andersen
    • Jens Kruse Andersen
      Sorry for not making a single post after completing computations. I have stopped now. ... The second (CP-10) is 16 times larger with gaps 28 and 2: 87873432313
      Message 2 of 4 , Feb 4 11:43 AM
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        Sorry for not making a single post after completing computations.
        I have stopped now.

        I wrote:
        > The first (CP-10) has gaps 16 and 14 (sum 5#):
        > 5373097559,5373097573,5373097589,5373097603,5373097619,
        > 5373097633,5373097649,5373097663,5373097679,5373097693

        The second (CP-10) is 16 times larger with gaps 28 and 2:
        87873432313 + 0,28,30,58,60,88,90,118,120,148

        A probably non-minimal (CP-11) with gaps 16 and 14:
        196723765163557 + 0,16,30,46,60,76,90,106,120,136,150

        And a probably non-minimal (CP-12) with gaps 14 and 16:
        438536033046239 + 0,14,30,44,60,74,90,104,120,134,150,164

        A (CP-13) must contain an AP6 inside an AP7. The common difference in an AP7
        not starting at 7 is always a multiple of 7# = 210.
        Inside the AP7 there has to be at least (210-2)*6 = 1248 simultaneous
        composites.
        That makes a (CP-13) computionally infeasible.
        If the numbers are small then 1248 composites is too hard.
        If the numbers are large then 13 primes is too hard.

        --
        Jens Kruse Andersen
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