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Smallest known CPAP-7 at 33 digits

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  • Jens Kruse Andersen
    Harvey Dubner has found the smallest known CPAP-7 with a program by me: 149143516628800164802930723713131 + 210n, n=0..6 The old record from 1997 was 37 digits
    Message 1 of 1 , May 4 11:53 AM
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      Harvey Dubner has found the smallest known CPAP-7 with a program by me:
      149143516628800164802930723713131 + 210n, n=0..6

      The old record from 1997 was 37 digits by Dubner alone.
      The difference in a CPAP-7 must be at least 210, meaning 209*6=1254 composites
      are required. This makes small CPAP-7 much harder than larger ones, and the
      minimal CPAP-7 currently seems out of reach.
      The expectation was 23 GHz days to find around 1 million AP-7 before a CPAP-7.
      The GMP library was used for prp testing and Marcel Martin's Primo proved the
      primes. Also thanks to Paul Zimmermann for discussions about the problem.

      The smallest known CPAP-k are listed here:
      http://hjem.get2net.dk/jka/math/cpap.htm#smallest
      Torbjörn Alm has earlier found the smallest known CPAP-8 with my program,
      without an announcement.
      Any CPAP-9 or -10 is hard and I have not heard of any searches for small cases.

      --
      Jens Kruse Andersen
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