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Re: nonprime?

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  • Mike Oakes
    ... to ... Using PFGW, I have found all those with
    Message 1 of 10 , Mar 1, 2007
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      --- In primenumbers@yahoogroups.com, "Paul Underwood"
      <paulunderwood@...> wrote:
      >
      > Enter 2^y-y into http://www.primenumbers.net/prptop/searchform.php
      to
      > see gigantic PrPs:
      >
      > 9 2^505431-505431 152150 Henri Lifchitz 04/2005
      > 10 2^500899-500899 150786 Henri Lifchitz 04/2005
      > 11 2^481801-481801 145037 Henri Lifchitz 03/2005
      > 108 2^228271-228271 68717 Henri Lifchitz 11/2004
      > 170 2^182451-182451 54924 Henri Lifchitz 10/2004
      > 509 2^108049-108049 32526 Henri Lifchitz 11/2001
      > 2527 2^61011-61011 18367 Henri Lifchitz 09/2001
      > 2534 2^60975-60975 18356 Henri Lifchitz 09/2001
      > 5891 2^44169-44169 13297 Henri Lifchitz 09/2001
      >
      > There may be more sub-giantic ones,

      Using PFGW, I have found all those with < 10000 digits:-

      2^2-2 prime by PFGW
      2^3-3 prime by PFGW
      2^9-9 prime by PFGW
      2^13-13 prime by PFGW
      2^19-19 prime by PFGW
      2^21-21 prime by PFGW

      2^55-55 prime by PRIMO 0s
      2^261-261 prime by PRIMO 0.06s
      2^3415-3415 prime by PRIMO 47mn 6s
      2^4185-4185 prime by PRIMO 2h 3mn 22s
      2^7353-7353 prime by PRIMO 23h 20mn 22s
      2^12213-12213 137-PRP by PFGW [PRIMO certification would take c. 6
      days]

      [
      BTW when Werner said:
      >Thanks to all! MuPAD confirms:
      >2^n-n is prime for n=3415, 4185, 7353.
      I think he was being optimistic, and should have said "probable
      prime", no?
      ]

      I've done the same for 2^n+n.

      Henri's site http://www.primenumbers.net/prptop/searchform.php
      gives:

      3 2^678561+678561 204268 Henri Lifchitz 05/2006
      137 2^204129+204129 61449 Henri Lifchitz 04/2002
      937 2^88071+88071 26513 Henri Lifchitz 09/2001

      so the first of these is the 3rd-largest PRP known.

      And to complete the picture, here are all those with < 10000 digits :-

      2^1+1 prime by PFGW
      2^3+3 prime by PFGW
      2^5+5 prime by PFGW
      2^9+9 prime by PFGW
      2^15+15 prime by PFGW

      2^39+39 prime by VFYPR 0 sec
      2^75+75 prime by VFYPR 0 sec
      2^81+81 prime by VFYPR 0 sec
      2^89+89 prime by VFYPR 0 sec
      2^317+317 prime by VFYPR 2 sec
      2^701+701 prime by VFYPR 60 sec
      2^735+735 prime by VFYPR 71 sec
      2^1311+1311 prime by VFYPR 1484 sec
      2^1881+1881 prime by VFYPR 11991 sec
      2^3201+3201 prime by PRIMO 48mn 23s
      2^3225+3225 prime by PRIMO 38mn 50s
      2^11795+11795 137-PRP by PFGW (PRIMO certification would take c. 5
      days)

      All timings are for a 1.2 GHz PC.

      Anyone want to do those 2 bigger certifications with PRIMO?

      -Mike Oakes
    • Christ van Willegen
      Hi, ... It took a bit less than 4 (CPU) days on my PC, but since I can only run it during working hours, and I took a week off, it took quite some (wall-clock)
      Message 2 of 10 , Mar 23, 2007
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        Hi,

        On 3/2/07, Mike Oakes <mikeoakes2@...> wrote:
        > 2^12213-12213 137-PRP by PFGW [PRIMO certification would take c. 6
        > days]

        It took a bit less than 4 (CPU) days on my PC, but since I can only
        run it during working hours, and I took a week off, it took quite some
        (wall-clock) time...

        [PRIMO - Primality Certificate]
        Version=2.3.1
        WebSite=http://www.ellipsa.net/
        Format=3
        ID=B2E4101C81D29
        Created=03-02-2007 08:18:24 am
        TestCount=498
        Status=Candidate certified prime

        [Running Times]
        Initialization=11.70s
        1stPhase=73h 34mn 19s
        2ndPhase=21h 45mn 27s
        Total=95h 19mn 58s

        [Candidate]
        File=C:\Christ\Primo 2.3.1\2^y-y.in
        Expression=2^12213-12213

        I'll start testing the + form Mike mentioned on Monday.

        The full cert will be published and checked soon.

        Have a good week-end!

        Christ van Willegen
      • Christ van Willegen
        Hi, Mike Oakes said: 2^11795+11795 137-PRP by PFGW (PRIMO certification would take c. 5 days) My computer says: [PRIMO - Task Report] Version=2.3.1
        Message 3 of 10 , Apr 10, 2007
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          Hi,

          Mike Oakes said:
          2^11795+11795 137-PRP by PFGW (PRIMO certification would take c. 5
          days)


          My computer says:
          [PRIMO - Task Report]
          Version=2.3.1
          WebSite=http://www.ellipsa.net/
          Task=Certification
          ID=B2E63036D59E4
          Created=04-05-2007 03:58:18 pm

          [Common]
          Path=C:\Christ\Primo 2.3.1\
          Selected=1
          Processed=1
          Certified=1
          Candidate #1=Certified, 94h 3mn 48s

          [Candidate #1]
          Input=primo-B2E5901A2ECA1-001.tmp
          Report=primo-B2E5901A2ECA1-001.cr
          Output=primo-B2E5901A2ECA1-001.out
          Status=Candidate certified prime


          So, both numbers have been proven prime.

          I'll run Cert_val on the second certificate and publish both after that.

          Christ van Willegen
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