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nonprime?

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  • Werner D. Sand
    Is 2^n-n nonprime for all n 261?
    Message 1 of 10 , Feb 26, 2007
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      Is 2^n-n nonprime for all n>261?
    • Richard FitzHugh
      2^3415-3415 is a probable prime (I don t have the software to do a full check on it) Richard ...
      Message 2 of 10 , Feb 26, 2007
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        2^3415-3415 is a probable prime (I don't have the software to do a full
        check on it)

        Richard


        >From: "Werner D. Sand" <Theo.3.1415@...>
        >To: primenumbers@yahoogroups.com
        >Subject: [PrimeNumbers] nonprime?
        >Date: Mon, 26 Feb 2007 17:44:15 -0000
        >
        >Is 2^n-n nonprime for all n>261?
        >

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      • Paul Underwood
        ... 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
        Message 3 of 10 , Feb 26, 2007
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          --- In primenumbers@yahoogroups.com, "Richard FitzHugh"
          <fitzhughrichard@...> wrote:
          >
          >
          > 2^3415-3415 is a probable prime (I don't have the software to do a full
          > check on it)
          >
          > Richard
          >
          >
          > >From: "Werner D. Sand" <Theo.3.1415@...>
          > >To: primenumbers@yahoogroups.com
          > >Subject: [PrimeNumbers] nonprime?
          > >Date: Mon, 26 Feb 2007 17:44:15 -0000
          > >
          > >Is 2^n-n nonprime for all n>261?
          > >
          >

          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,

          Paul
        • Paul Underwood
          ... Marcel Martin recently de-restricted Primo and his program will prove this one: http://www.ellipsa.net/ (If you need to over 10k bits use an older
          Message 4 of 10 , Feb 26, 2007
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            --- In primenumbers@yahoogroups.com, "Richard FitzHugh"
            <fitzhughrichard@...> wrote:
            >
            >
            > 2^3415-3415 is a probable prime (I don't have the software to do a full
            > check on it)
            >
            > Richard

            Marcel Martin recently de-restricted Primo and his program will prove
            this one:

            http://www.ellipsa.net/

            (If you need to over 10k bits use an older version.)

            Paul
          • Mike Oakes
            ... full ... On a 1.2GHz PC, Marcel Martin s marvellous, magical PRIMO program (do try it if you haven t already!) gave this:- [PRIMO - Task Report]
            Message 5 of 10 , Feb 26, 2007
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              --- In primenumbers@yahoogroups.com, "Richard FitzHugh"
              <fitzhughrichard@...> wrote:
              >
              > 2^3415-3415 is a probable prime (I don't have the software to do a
              full
              > check on it)
              >

              On a 1.2GHz PC, Marcel Martin's marvellous, magical PRIMO program (do
              try it if you haven't already!) gave this:-

              [PRIMO - Task Report]
              Version=2.2.0 beta 7
              WebSite=http://www.ellipsa.net/
              Task=Certification
              ID=B2E3E046E58C6
              Created=02/26/2007 08:39:00 pm

              [Common]
              Path=C:\PRIMO\work\
              Selected=1
              Processed=1
              Certified=1
              Candidate #1=Certified, 47mn 6s

              [Candidate #1]
              Input=mike.in
              Report=primo-B2E3E046E58C6-001.cr
              Output=primo-B2E3E046E58C6-001.out
              Status=Candidate certified prime

              -Mike Oakes
            • Richard FitzHugh
              Is there a simple-to-run elliptic curve-based primality-proving programme available for Mac OS X? The only ones I seem to be able to find are for Windows
              Message 6 of 10 , Feb 26, 2007
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                Is there a simple-to-run elliptic curve-based primality-proving programme
                available for Mac OS X? The only ones I seem to be able to find are for
                Windows platform...

                Thanks

                Richard


                >From: "Mike Oakes" <mikeoakes2@...>
                >To: primenumbers@yahoogroups.com
                >Subject: [PrimeNumbers] Re: nonprime?
                >Date: Mon, 26 Feb 2007 21:38:50 -0000
                >
                >--- In primenumbers@yahoogroups.com, "Richard FitzHugh"
                ><fitzhughrichard@...> wrote:
                > >
                > > 2^3415-3415 is a probable prime (I don't have the software to do a
                >full
                > > check on it)
                > >
                >
                >On a 1.2GHz PC, Marcel Martin's marvellous, magical PRIMO program (do
                >try it if you haven't already!) gave this:-
                >
                >[PRIMO - Task Report]
                >Version=2.2.0 beta 7
                >WebSite=http://www.ellipsa.net/
                >Task=Certification
                >ID=B2E3E046E58C6
                >Created=02/26/2007 08:39:00 pm
                >
                >[Common]
                >Path=C:\PRIMO\work\
                >Selected=1
                >Processed=1
                >Certified=1
                >Candidate #1=Certified, 47mn 6s
                >
                >[Candidate #1]
                >Input=mike.in
                >Report=primo-B2E3E046E58C6-001.cr
                >Output=primo-B2E3E046E58C6-001.out
                >Status=Candidate certified prime
                >
                >-Mike Oakes
                >

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              • Werner D. Sand
                ... Thanks to all! MuPAD confirms: 2^n-n is prime for n=3415, 4185, 7353. Werner
                Message 7 of 10 , Feb 27, 2007
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                  --- In primenumbers@yahoogroups.com, "Werner D. Sand" <Theo.3.1415@...>
                  wrote:
                  >
                  > Is 2^n-n nonprime for all n>261?
                  >

                  Thanks to all! MuPAD confirms:
                  2^n-n is prime for n=3415, 4185, 7353.
                  Werner
                • Mike Oakes
                  ... to ... Using PFGW, I have found all those with
                  Message 8 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 9 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 10 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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