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CPAP-3 with 6091 digits

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  • Jens Kruse Andersen
    The largest known CPAP-3 (3 consecutive primes in arithmetic progression) is now: 4811*2^20219 -7475, -3737, +1 (6091 digits) The easily provable
    Message 1 of 1 , Jun 28, 2004
      The largest known CPAP-3 (3 consecutive primes in arithmetic
      progression) is now:
      4811*2^20219 -7475, -3737, +1 (6091 digits)

      The easily provable 4811*2^20219+1 was found by Patrick Demichel.
      My sieve and PrimeForm/GW found the two other numbers to be probable primes.
      Christ van Willegen proved 4811*2^20219-7475 with Marcel Martin's Primo.
      Hans Rosenthal proved 4811*2^20219-3737 with Primo.

      Jim Fougeron's Cert_Val has validated the certificates.
      Certificates and certification reports are in a 5 MB zip file linked at
      The Largest Known CPAP's:
      http://hjem.get2net.dk/jka/math/cpap.htm#k3

      The certifications should become 5th and 6th in the Primo Top-20:
      http://www.ellipsa.net/primo/top20.html

      Primo version 2.2.0 beta 1 was used for both primes.
      4811*2^20219-7475 took 197 days on a 1.8 GHz Pentium 4.
      4811*2^20219-3737 took 57 days on a 2 GHz Athlon XP 2400+.
      The difference is huge. It is almost as large for phase 2 as phase 1:

      Expression=4811*2^20219-7475
      [Running Times]
      Initialization=5mn 13s
      1stPhase=4024h 16mn 53s
      2ndPhase=704h 29mn 42s
      Total=4728h 51mn 48s

      Expression=4811*2^20219-3737
      [Running Times]
      Initialization=1mn 8s
      1stPhase=1158h 25mn 27s
      2ndPhase=217h 5mn 43s
      Total=1375h 32mn 19s

      The certification reports show the number of backtracks and runs above 1.
      This difference is small between the two certifications.
      4811*2^20219-7475: 896 tests found on run 1, two on run 2, one on run 3.
      Subtracting the 54 backtracks leaves the 845 tests in the final certificate.
      4811*2^20219-3737: 935 tests found on run 1, one on run 2.
      Subtracting 55 backtracks leaves 881 tests.

      We guess the huge time difference is mainly caused by much better Athlon
      performance in Primo.

      --
      Jens Kruse Andersen
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