Loading ...
Sorry, an error occurred while loading the content.

Primes in Arithmetic Progression Records

Expand Messages
  • Jens Kruse Andersen
    I have made a new record page: Primes in Arithmetic Progression Records http://hjem.get2net.dk/jka/math/aprecords.htm It has the single largest known AP-k for
    Message 1 of 1 , Jan 24, 2005
    • 0 Attachment
      I have made a new record page:
      Primes in Arithmetic Progression Records
      http://hjem.get2net.dk/jka/math/aprecords.htm

      It has the single largest known AP-k for all k, plus a record history and the
      smallest AP-k with minimal difference.
      Comments are welcome.
      Have I overlooked an existing page?
      I searched the Internet and the best found results for different lengths were
      spread in 5 different places.

      The only found results between 1037-digit AP8 and 18-digit AP20 were 3 special
      type AP's:
      101-digit CPAP-9, 93-digit CPAP-10, and a 22-digit AP17 starting at 17.
      They are good results for their type but not for arbitrary AP's.
      The AP17 held all found records down to AP11. Has no AP11 above 22 digits been
      published?
      The influence of the titanic limit in the Prime Pages seems big.

      I have set easy but not completely trivial records for AP9 to AP19.
      At least they are larger than the records for k "simultaneous" primes, except
      the AP18.
      If you find larger AP's, let me know.

      AP9: same as AP10
      AP10: (501788528 + 12970338*n)*463#+1, n=0..9 (202 digits)

      AP11: (262779044 + 49839897*n)*281#+1, n=0..10 (125 digits)

      AP12: (8986417 + 30820926*n)*157#+1, n=0..11 (71 digits)

      AP13: (539591312 + 45914254*n)*103#+1, n=0..12 (50 digits)

      AP14: same as AP15
      AP15: (358766428 + 17143877*n)*101#+1, n=0..14 (48 digits)

      AP16: same as AP17
      AP17: (253456539 + 13892183*n)*43#+1, n=0..16 (25 digits)

      AP18: same as AP19
      AP19: (273972449 + 25355830*n)*31#+1, n=0..18 (21 digits)

      The GMP library made all prp tests. PrimeForm/GW proved all primes.

      The AP19 was the first AP of length at least 16 in that search.
      If only such luck had struck in my failed search for the first AP23.

      --
      Jens Kruse Andersen
    Your message has been successfully submitted and would be delivered to recipients shortly.