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Re: [PrimeNumbers] Re: Twin Record

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  • 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 1 of 6 , Sep 28, 2002
      > 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 2 of 6 , Sep 28, 2002
        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 3 of 6 , Sep 28, 2002
          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 4 of 6 , Sep 28, 2002
            > 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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