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A gigantic AP-4

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  • mikeoakes2@aol.com
    Here is a new AP4 record at 10004 digits:- (2024725+197732*n)*23159#+1 is prime for n=0..3 All confirmed prime with PFGW -tc This displaces David s 7534-digit
    Message 1 of 133 , Dec 16, 2006
      Here is a new AP4 record at 10004 digits:-

      (2024725+197732*n)*23159#+1 is prime for n=0..3

      All confirmed prime with PFGW -tc

      This displaces David's 7534-digit record which, having stood for nearly
      2 years, was the 4th-longest surviving AP-n record, as Jens's page
      shows:
      http://hjem.get2net.dk/jka/math/aprecords.htm

      Input/output statistics:-
      Numbers tested by NewPGen: 3*10^6
      NewPGen reduced these (by sieving to 0.3T) to: 1.18*10^6
      Numbers tested by PFGW: 985451
      PRP's found by PFGW: 1939
      AP3's found: 690
      AP4's found: 1

      Run-time statistics:-
      NewPGen: 13.5 GHz-days
      PFGW: 340 GHz-days
      Pascal program to find AP's: 2 GHz-secs

      Poisson was slightly favourable: about 1200 AP3's (which would have
      required about 1939*sqrt(1200/690)=2560 PRPs) was the expected number
      needed to get an AP4.

      1939 gigantic PRPs is quite a lot to have had to find: if they had
      (only) been PRPs they would have pushed me to Rank 2 on Henri's page:
      http://www.primenumbers.net/prptop/topdisc.php
      and would have increased the world's stockpile of gigantic PRPs by 14%.
      But alas, they are all provable.

      -Mike Oakes
    • andrey_601
      ... http://mat.fc.ul.pt/ind/ncpereira/Bounds%20for%20Th,Ps,Ga,Ri.pdf And some further excursions of the related function:
      Message 133 of 133 , May 15, 2010
        > Let puzzle(n) = sqrt(n)*(1 - log(n#)/n)
        >
        > Puzzle 1: Try to find a prime, p_min, such that
        > puzzle(p_min) < puzzle(110102617)
        >
        > Puzzle 2: Try to find a prime, p_max, such that
        > puzzle(p_max) > puzzle(19373)

        http://mat.fc.ul.pt/ind/ncpereira/Bounds%20for%20Th,Ps,Ga,Ri.pdf

        And some further excursions of the related function:
        http://www.primefan.ru/stuff/primes/table.html
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