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

Re: [primeform] New gigantic AP-4

Expand Messages
  • Jens Kruse Andersen
    ... The current status page shows a 10043-digit AP4 by Ken Davis: (97070894 + 104086947*n)*2^33333+1, n=0..3 It s the second largest known with unfortunate
    Message 1 of 133 , Aug 15, 2007
      July 27 I wrote:
      > Congratulations to Jim Fougeron for
      > (18271126 + 9548007*n)*2^35000+1, n = 0..3 (10544 digits)
      >
      > I saw it at http://primes.utm.edu/primes/status.php and have updated
      > http://hjem.get2net.dk/jka/math/aprecords.htm

      The current status page shows a 10043-digit AP4 by Ken Davis:
      (97070894 + 104086947*n)*2^33333+1, n=0..3
      It's the second largest known with unfortunate timing.
      The search probably started before Jim's discovery.
      Unlike most other prime searches, this cannot start over
      at another size without losing a lot more work than sieving.
      Congratulations anyway. Gigantic AP4's are impressive.

      I have set 3 easier records with prp tests by the GMP library:
      69-digit AP14: (1067385825+193936257*n)*151#+1, n=0..13
      29-digit AP17: (1259891250+70154768*n)*53#+1, n=0..16
      29-digit AP18: (1051673535+32196596*n)*53#+1, n=0..17

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