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Re: Twin Record

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  • David Broadhurst
    ... Wow! On merely the 6th Proth-find, it seems: 818 12522105*2^169690-1 51089 g259 2002 819 9335097*2^169690-1 51089 g259 2002 820
    Message 1 of 6 , Sep 28, 2002
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      > 9999 33218925*2^169690-1 51090 g259 02 Twin #0209
      > 9999 33218925*2^169690+1 51090 g259 02 Twin #0209

      Wow!

      On merely the 6th Proth-find, it seems:

      818 12522105*2^169690-1 51089 g259 2002
      819 9335097*2^169690-1 51089 g259 2002
      820 151737*2^169690+1 51087 g259 2002
      9999 31809147*2^169690-1 51090 g259 02 #0209
      9999 32596143*2^169690-1 51090 g259 02 #0209
      9999 33218925*2^169690-1 51090 g259 02 Twin #0209
      9999 33218925*2^169690+1 51090 g259 02 Twin #0209

      unless Daniel Papp has a huge backlog of g259
      Proth-finds to post.

      But then, think of all those Proth cycles
      looking for plain top5000 cannon fodder.

      Someone has to strike it lucky, some time.

      Congrats to Daniel!

      It's amusing that the twin and triplet records
      fell on successive days:

      http://groups.yahoo.com/group/primeform/message/2723

      the latter falling twice:

      http://groups.yahoo.com/group/primeform/message/2724

      this second being my bit of luck
      (but the first was gotten by paying
      the expected Poisson dues)

      David
    • Yves Gallot
      ... Daniel Papp used the classical method for his discovery (http://www.utm.edu/research/primes/bios/titans/Papp.html) i.e. NewPGen+PRP+Proth The expected
      Message 2 of 6 , Sep 28, 2002
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        > Wow!
        >
        > On merely the 6th Proth-find, it seems:
        > unless Daniel Papp has a huge backlog of g259
        > Proth-finds to post.
        >
        > But then, think of all those Proth cycles
        > looking for plain top5000 cannon fodder.

        Daniel Papp used the 'classical' method for his discovery
        (http://www.utm.edu/research/primes/bios/titans/Papp.html)
        i.e. NewPGen+PRP+Proth

        The expected number of twins in 3-33,218,925 for n=169690 is
        Sum [k odd = 3 to 33218925] 1.32 * (2 / log(k*2^169690))^2 = 0.006.

        The first twin was expected for k=5,000,000,000 !

        But if 200 people are searching for a twin prime record around n=169690,
        then 33,218,925 was the expected k.

        Yves
      • David Broadhurst
        Thanks for the twin heuristics, Yves. Apologies to Daniel; his bio indeed recounts that he was smart as well as very lucky. Given his NewPGen sieve, it would
        Message 3 of 6 , Sep 28, 2002
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          Thanks for the twin heuristics, Yves.

          Apologies to Daniel; his bio indeed recounts
          that he was smart as well as very lucky.

          Given his NewPGen sieve, it would need
          David Underbakke to say just how lucky.

          Meanwhile the triplet record crept up.

          First I found a 7-11-13 BLS triplet a shade low:

          http://groups.yahoo.com/group/primeform/message/2725

          and then another just a shade bigger
          than the day-old 5-7-11 record:

          http://groups.yahoo.com/group/primeform/message/2726.

          The heuristics of this

          twin-seed ==> quintuple sieve ==> 3 goes at a triplet

          method are hairy to compute, but I think
          I was lucky by a factor of about 2.

          My Poissonian guess was a mean somewhere between
          1 and 2 hits and I got 4.

          But maybe I screwed up the heuristics;
          it entailed a fiendish 5-fold filter, hand crafted
          in base 35 and written in ForTran (of course).

          Anyway, I ain't complaining about the 4 hits instead of 2 :-)

          David
        • David Underbakke
          I would also like to add my congratulations to Daniel on his new twin prime record. I hope the discovery leaves him smiling for a very long time. My comments
          Message 4 of 6 , Sep 28, 2002
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            I would also like to add my congratulations to Daniel on his new twin prime
            record. I hope the discovery leaves him smiling for a very long time.

            My comments on luck below should not detract from the fact that Daniel chose
            an intelligent course of action and achieved his goal. It is the discovery
            that is the goal and reward, not the number of attempts along the way.
            There is a certain amount of luck in any twin prime/Sophie Germain discovery.

            I was just as happy finding 318032361.2^107001+/-1 with only 60 primes found
            (very lucky) as I was finding 1807318575.2^98305+/-1 after finding nearly
            1000 primes (expected primes). (Both efforts with Phil Carmody)

            Daniel, be very very happy with your discovery. You have achieved an
            important goal that will be in the top twenty pages for a very long time.

            Yves Gallot wrote:

            >The expected number of twins in 3-33,218,925 for n=169690 is
            >Sum [k odd = 3 to 33218925] 1.32 * (2 / log(k*2^169690))^2 = 0.006.
            >
            >The first twin was expected for k=5,000,000,000 !
            >
            >But if 200 people are searching for a twin prime record around n=169690,
            >then 33,218,925 was the expected k.
            >

            I would elaborate on this. If 200 people are searching, then 1 of those 200
            people would find a twin by searching a range of 33,218,925 assuming that
            each one was searching a different n value. That is still a 0.5% chance
            that a specific individual would find it in that range.

            David Broadhurst wrote:

            >Thanks for the twin heuristics, Yves.
            >
            >Apologies to Daniel; his bio indeed recounts
            >that he was smart as well as very lucky.
            >
            >Given his NewPGen sieve, it would need
            >David Underbakke to say just how lucky.
            >

            All the discussions already include the assumption that a good sieve was
            applied before PRP testing. To find a twin prime larger than Daniel's
            record, I will have to use 10 Ghz of processing for 3-4 years to have a
            better than even chance.

            Anyone who is willing to make that commitment should get full credit for the
            discovery no matter when it happens. I give Daniel full credit for his
            discovery, as indicated at the start of this message.

            ___________

            David Underbakke
          • Andrey Kulsha
            ... Amazing. It make me think of 1/lg2=3.321928... :-) Best wishes, Andrey
            Message 5 of 6 , Sep 28, 2002
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              > 9999 33218925*2^169690-1 51090 g259 02 Twin #0209
              > 9999 33218925*2^169690+1 51090 g259 02 Twin #0209

              Amazing.

              It make me think of 1/lg2=3.321928... :-)

              Best wishes,

              Andrey
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