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C(x,6)+1

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  • Jens Kruse Andersen
    p = C(342397*2^36022+4,6)+1 is a binomial prime with 65093 digits. It was found and proved with PrimeForm/GW. Earlier David found a top-5000 prime C(x,4)+1
    Message 1 of 2 , Nov 17 3:30 PM
      p = C(342397*2^36022+4,6)+1 is a binomial prime with 65093 digits.
      It was found and proved with PrimeForm/GW.
      Earlier David found a top-5000 prime C(x,4)+1 with a different method:
      http://groups.yahoo.com/group/primeform/message/6036
      The next logical challenge would be C(x,8)+1 which looks harder.

      If 2 out of 6 consecutive numbers are completely factored
      then a prp on form C(x,6)+1 just becomes BLS provable.
      My lucky search went through the Prime Pages database with p of top-5000 size.
      Thanks to Chris for maintaining the database. It has been very helpful before.
      342397*2^36022+1 was found by Vincent S. Wighman with Proth.exe in 1998.
      That helper enabled the 33.34% proof:

      D:>pfgw -t -hhelper.txt c6.txt
      PFGW Version 1.2.0 for Windows [FFT v23.8]

      Primality testing (342397*2^36022+4)*(342397*2^36022+3)*(342397*2^36022+2)*
      (342397*2^36022+1)*(342397*2^36022)*(342397*2^36022-1)/6!+1
      [N-1, Brillhart-Lehmer-Selfridge]
      Reading factors from helper file helper.txt
      Running N-1 test using base 5
      Calling Brillhart-Lehmer-Selfridge with factored part 33.34%
      (342397*2^36022+4)*(342397*2^36022+3)*(342397*2^36022+2)*(342397*2^36022+1)*
      (342397*2^36022)*(342397*2^36022-1)/6!+1 is prime! (2620.8548s+0.0162s)

      PrimeForm cannot parse C(x,y) for x>2^31 so a longer expression was used.

      --
      Jens Kruse Andersen
    • David Broadhurst
      Jens, ... Excellent! I do like your ideas for reprocessing the list. David
      Message 2 of 2 , Nov 17 4:22 PM
        Jens,

        > My lucky search went through the Prime Pages database with
        > p of top-5000 size.

        Excellent! I do like your ideas for reprocessing the list.

        David
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