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14133RE: [PrimeNumbers] Generalised factorial primes??

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  • cino hilliard
    Dec 5, 2003
    • 0 Attachment
      Hi all,
      I just joined the group. I found it searching for a solution to a prime
      problem I had and am
      trying to prove. This caught my interest so i though i would chime in.


      >From: "julienbenney" <jpbenney@...>
      >To: primenumbers@yahoogroups.com
      >Subject: [PrimeNumbers] Generalised factorial primes??
      >Date: Fri, 05 Dec 2003 11:32:54 -0000
      >
      >Using the ordinary equipment on my old home computer, I found that (13!
      >+ 2)/2 is prime.
      >
      >How many primes of the form (a! + n)/n [or (a! - n)/n] are actually
      >known? Do you think there might by many to be found??
      Yes Many possiblt infinite. But watch out

      From the Pari script below.
      Here is a list n =1,2..50 and n=1,2 for sums

      a n (a! + n)/n
      1,1,2,
      2,1,3,
      2,2,2,
      3,1,7,
      4,2,13,
      5,2,61,
      7,2,2521,
      8,2,20161,
      11,1,39916801,
      13,2,3113510401,
      16,2,10461394944001,
      27,1,10888869450418352160768000001,
      30,2,132626429906095529318154240000001,
      37,1,13763753091226345046315979581580902400000001,
      41,1,33452526613163807108170062053440751665152000000001,
      43,2,30207631531686917818677566034256998753632256000000001,
      49,2,304140932017133780436126081660647688443776415689605120000000001,

      Another list for n = 1,2..50 for diff
      a n (a! - n)/n
      3,1,5,
      3,2,2,
      4,1,23,
      4,2,11,
      5,2,59,
      6,1,719,
      6,2,359,
      7,1,5039,
      9,2,181439,
      12,1,479001599,
      14,1,87178291199,
      30,1,265252859812191058636308479999999,
      31,2,4111419327088961408862781439999999,
      32,1,263130836933693530167218012159999999,
      33,1,8683317618811886495518194401279999999,
      38,1,523022617466601111760007224100074291199999999,
      41,2,16726263306581903554085031026720375832575999999999,

      Pari Script.
      nfactp2d2(n,m) =
      {
      for(x=1,n,
      for(k=1,m,
      y=floor((x!+ k)/k);
      if(isprime(y),print(x","k","y","))
      )
      )
      }
      nfactm2d2(n,m) =
      {
      for(x=1,n,
      for(k=1,m,
      y=floor((x!- k)/k);
      if(isprime(y),print(x",",k","y","))
      )
      )
      }
      If you dont have Pari I recommend it over all the expensive programs
      Maple,Mathematica etc
      it is free and available at

      http://pari.math.u-bordeaux.fr/

      Also, it has prime proving capability isprime() in addition to the much
      faster ispseudoprime.
      The script language is c-like but much better than c in terms of use and of
      course number
      theory capability.

      I don't know what your system is but if it is windows, I recommend you
      download the binary
      executable Pari.exe that will build all the files and folders for you. You
      will need to modify the
      environment path to include c:\program files\pari; This will enable you to
      call gp.exe from other
      folders.

      I submitted some sequences to sloane's and referenced this email and your
      question.

      Have fun in Primelandia
      Cino

      Behind some primes are other primes
      with other primes behind um.
      And behind these primes
      are still more primes
      and so ad infinitum.

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