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New Cullen Record

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  • Mark Rodenkirch
    I am pleased to annouce that I found the largest known Cullen prime and it comes just a few weeks after my recent Woodall prime record and seven years after
    Message 1 of 6 , Aug 25, 2005
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      I am pleased to annouce that I found the largest known Cullen prime
      and it comes just a few weeks after my recent Woodall prime record and
      seven years after the previous record.

      1354828*2^1354828+1 is 407850 digits long

      It was found using my MultiSieve program for sieving and Jean Penne's
      LLR for the primality test. Once verified it should be #35 in Chris
      Caldwell's list.

      Of note, I sieved with a version of MultiSieve that I ported to
      PowerPC as it can sieve Cullens/Woodalls many times deeper than x86 as
      it has many 64-bit registers.

      --Mark
    • Jean PennĂ©
      Congrats, Mark ; the previous record is smashed !! Perhaps you might now be prompted to make a Multisieve version allowing distributed sieving, in order to go
      Message 2 of 6 , Aug 28, 2005
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        Congrats, Mark ; the previous record is smashed !!
        Perhaps you might now be prompted to make a Multisieve version
        allowing distributed sieving, in order to go further ?

        Best Regards,
        Jean

        --- In primenumbers@yahoogroups.com, "Mark Rodenkirch" <mgrogue@w...>
        wrote:
        > I am pleased to annouce that I found the largest known Cullen prime
        > and it comes just a few weeks after my recent Woodall prime record
        and
        > seven years after the previous record.
        >
        > 1354828*2^1354828+1 is 407850 digits long
        >
        > It was found using my MultiSieve program for sieving and Jean
        Penne's
        > LLR for the primality test. Once verified it should be #35 in Chris
        > Caldwell's list.
        >
        > Of note, I sieved with a version of MultiSieve that I ported to
        > PowerPC as it can sieve Cullens/Woodalls many times deeper than x86
        as
        > it has many 64-bit registers.
        >
        > --Mark
      • mgrogue@wi.rr.com
        ... The gain would be minimal because the sieve doesn t (and can t AFAIK) use a discrete log. You double the size of the range and the time to sieve will
        Message 3 of 6 , Aug 29, 2005
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          > Congrats, Mark ; the previous record is smashed !!
          > Perhaps you might now be prompted to make a Multisieve version
          > allowing distributed sieving, in order to go further ?
          >
          > Best Regards,
          > Jean

          The gain would be minimal because the sieve doesn't (and can't AFAIK)
          use a discrete log. You double the size of the range and the time to
          sieve will almost double.

          --Mark
        • eharsh82
          Mark, I think what Jean meant was that multiple people could work on different factor values for the same range of numbers. For example how PSP does
          Message 4 of 6 , Sep 14, 2005
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            Mark,
            I think what Jean meant was that multiple people could work on
            different factor values for the same range of numbers. For example how
            PSP does distributed sieving on its numbers.

            Secondly is there a MAC version for multisieve available. I have a G5
            sitting around, may be I can put it to some use.

            Lastly congrats for the prime! (Since the program uses my improvements
            I guess I get part of the credit :))

            Harsh




            --- In primenumbers@yahoogroups.com, mgrogue@w... wrote:
            > > Congrats, Mark ; the previous record is smashed !!
            > > Perhaps you might now be prompted to make a Multisieve version
            > > allowing distributed sieving, in order to go further ?
            > >
            > > Best Regards,
            > > Jean
            >
            > The gain would be minimal because the sieve doesn't (and can't AFAIK)
            > use a discrete log. You double the size of the range and the time to
            > sieve will almost double.
            >
            > --Mark
          • Phil Carmody
            ... This is a crime against primality! Phil () ASCII ribbon campaign () Hopeless ribbon campaign / against HTML mail / against gratuitous
            Message 5 of 6 , Sep 15, 2005
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              --- primenumbers@yahoogroups.com wrote:
              > From: "eharsh82" <harsh@...>
              ...
              > I have a G5 sitting around

              This is a crime against primality!

              Phil

              () ASCII ribbon campaign () Hopeless ribbon campaign
              /\ against HTML mail /\ against gratuitous bloodshed

              [stolen with permission from Daniel B. Cristofani]

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            • mgrogue@wi.rr.com
              ... My point is that you won t be able to sieve much deeper by taking a larger range and distributing it. Maybe you can sieve 1% or 2% deeper, but that
              Message 6 of 6 , Sep 15, 2005
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                > I think what Jean meant was that multiple people could work on
                > different factor values for the same range of numbers. For example
                > how PSP does distributed sieving on its numbers.

                My point is that you won't be able to sieve much deeper by taking a
                larger range and distributing it. Maybe you can sieve 1% or 2%
                deeper, but that doesn't make it worth the effort. The reason is
                that MultiSieve has to use trial division (at least for Cullen/Woodalls).
                PSP sieving gets a huge advantage because it uses a discrete log.

                > Secondly is there a MAC version for multisieve available. I have a
                > G5 sitting around, may be I can put it to some use.

                I've been working on one in my spare time. I used a Mac version to
                sieve the Cullen range in which I found the prime since I could sieve
                much deeper than a P4 could.

                In the meantime, head over to the pies_project and use your Mac to
                find a new 100000 digit prime.

                --Mark
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