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

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  • 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 1 of 4 , Feb 4, 2005
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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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