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CPAP-7 record

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  • Jens Kruse Andersen
    Torbjörn Alm has found the 3 largest known CPAP-7 (7 consecutive primes in arithmetic progression): a*460# + x + 210n, n=0..6 (201 digits) for a =
    Message 1 of 1 , Sep 2, 2003
      Torbjörn Alm has found the 3 largest known CPAP-7 (7 consecutive primes in
      arithmetic progression):

      a*460# + x + 210n, n=0..6 (201 digits)
      for a = 7032468079552, 7091037255023 and 7127829789350
      where x is the 177-digit constant:
      248780094097472243404896912185202045231738914942652056718577\
      710540347657189933931692656963039429596697403345980150176975\
      651015797243607875744813349096932598456481621971387004081

      Congratulations to Torbjörn on this top-3!
      He used my program and I also ran it but only found CPAP-6's.
      The GMP library was used for prp testing.
      All primes were proved with Tony Forbes' VFYPR.

      The old CPAP-7 record was 97 digits but the new is larger than the 7-tuplet
      record at 178 digits.
      A CPAP-7 must have a multiple of 7# = 210 as the difference between the primes
      to avoid divisibility by 2, 3, 5 and 7. This requires at least 209*6 = 1254
      intermediate composites and would usually be harder than a 7-tuplet.
      However the program computed a certain set of modular equations for all primes
      <= 433 (the 4 extra primes up to 460 were not necessary). The constant x was
      then computed to satisfy the equations. This guaranteed that the 1254 numbers
      all had a factor <= 433, so any AP-7 would also be CPAP-7.

      The expectation would be 6 days for my Athlon 1500+ alone. We were above
      expectation for 3 monitored pc's when the only unmonitored pc was checked
      after some days and showed 3 solutions!

      --
      Jens Kruse Andersen
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