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Definitive answer to post 10359 19 Dec 2002

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  • Ken Davis
    Hi All, Long long ago 19 Dec 2002 (post 10359) Sebastián Martín Ruiz asked Let F(n)=P(n)!-P(n)!!+2 P(n) n-th prime F(1)=2 Prime F(2)=5 Prime F(3)=107 Prime
    Message 1 of 1 , Aug 30, 2004
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      Hi All,
      Long long ago 19 Dec 2002 (post 10359) Sebastián Martín Ruiz asked

      Let F(n)=P(n)!-P(n)!!+2

      P(n) n-th prime


      F(1)=2 Prime
      F(2)=5 Prime
      F(3)=107 Prime
      F(4)=4937 Prime

      Find another prime number in this secuence

      to which I replied (without proof as I could only show that it was
      Fermat and Lucas PRP)
      (1667!)-(1667!2)+2
      However as it has 4650 digits I thought it should be provable.
      David Broadhurst pointed me to Marcel Martin's Primo (a marvellous
      program).

      I started primo 2.0.0 on 1667!-1667!2+2 and left it for what I
      thought
      would be 6-12 months.
      It has finished after "only" 1340h 11mn 39s
      the result being

      [PRIMO - Task Report]
      Version=2.0.0 - beta 3
      Task=Certification
      ID=B285E020B5C1A
      Created=01/15/2003 09:31:38 AM

      [Common]
      Path=C:\Program Files\Primo200\f1667\
      Selected=1
      Processed=1
      Certified=0
      Candidate #1=Failed, 1340h 11mn 39s

      [Candidate #1]
      Input=Primo-B284302D531FB-001.tmp
      Output=Primo-B284302D531FB-001.tmp
      Status=Failed, impossible to certify current N

      Not! what I was hoping for.

      Changes to Primo made it worthwhile trying again
      This time Primo sucessfully proved 1667!-1667!2+2 Prime

      [PRIMO - Primality Certificate]
      Version=2.2.0 beta 3
      WebSite=http://www.ellipsa.net/
      Format=3
      ID=B2A0002ACB343
      Created=03/08/2004 12:29:39 PM
      TestCount=614
      Status=Candidate certified prime

      [Running Times]
      Initialization=1mn 46s
      1stPhase=2071h 22mn 47s
      2ndPhase=563h 45mn 34s
      Total=2635h 10mn 8s

      [Candidate]
      File=D:\Primo220\wrk\f1667\f1667.in
      Expression=1667!-1667@2+2

      Cheers
      Ken
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