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Re: 2 > exp(Euler)

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  • mikeoakes2
    ... There was one remaining inaccuracy here: I only gave the sieving depth to a rounded value of 50 billion. I have just done another NewPGen sieve and
    Message 1 of 22 , Sep 26, 2009
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      --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
      >
      > You were within 2 sigma of theory:
      >
      > \p6
      > pr109=1;forprime(q=2,109,pr109*=q);km=2*10^9;p=5*10^10;
      > tried=393614016;found=140719122;hitrate=1.*found/tried;
      > theory=exp(Euler)*log(p)*intnum(k=1,km,1/log(k*pr109))/km;
      > test=hitrate/theory;sigm=(test-1)*sqrt(found);
      > print([hitrate,theory,test,sigm])
      >
      > [0.357505, 0.357450, 1.00015, 1.82364]
      >
      > The fidelity with theory is now wonderful.
      >
      > Your AP15 project measured exp(Euler) to better
      > than 2 parts in 10^4, in 3 GHz-days.

      There was one remaining inaccuracy here: I only gave the sieving depth to a rounded value of 50 billion.

      I have just done another NewPGen sieve and recorded the exact depth. After pfgw'ing (combined processing time < 1 GHz-day), the figures are very satisfactory, as sigma is down from 1.82 to 1.53:-

      \p6
      pr83=1;forprime(q=2,83,pr83*=q);km=2*10^9;p=50066810303;
      tried=370597641;found=171068264;hitrate=1.*found/tried;
      theory=exp(Euler)*log(p)*intnum(k=1,km,1/log(k*pr83))/km;
      test=hitrate/theory;sigm=(test-1)*sqrt(found);
      print([hitrate,theory,test,sigm])

      [0.461601, 0.461547, 1.00012, 1.52844]

      Mike
    • djbroadhurst
      ... Great stuff, Mike. There is a corollary: both NewPgen and OpenPFGW must have been behaving near perfectly to give such wondrous agreement with Mertens,
      Message 2 of 22 , Sep 26, 2009
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        --- In primenumbers@yahoogroups.com,
        "mikeoakes2" <mikeoakes2@...> wrote:

        > [0.461601, 0.461547, 1.00012, 1.52844]

        Great stuff, Mike.

        There is a corollary: both NewPgen and OpenPFGW
        must have been behaving near perfectly to give
        such wondrous agreement with Mertens, nicht wahr?

        PS: How long will Pascal take for the AP16 :-?

        David
      • mikeoakes2
        ... Dang.., I hoped no-one (at least not one of my APn competitors:-) would spot what that NewPGen run was for; but you of course got it in one. On an Intel
        Message 3 of 22 , Sep 26, 2009
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          --- In primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:
          >
          > PS: How long will Pascal take for the AP16 :-?

          Dang.., I hoped no-one (at least not one of my APn competitors:-) would spot what that NewPGen run was for; but you of course got it in one.

          On an Intel Quad at 3.6Ghz, about 4 months elapsed if I'm lucky, twice that if not.

          (Current status: after 10 elapsed hours, it has found 7 AP13's.)

          Mike
        • djbroadhurst
          ... Oh what a tangled web remains, When author candidly explains! David, pace Marmion http://www.quotationspage.com/quote/27150.html
          Message 4 of 22 , Sep 26, 2009
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            --- In primenumbers@yahoogroups.com,
            "mikeoakes2" <mikeoakes2@...> wrote:

            > Dang.., I hoped no-one
            > (at least not one of my APn competitors:-)
            > would spot what that NewPGen run was for;
            > but you of course got it in one.

            Oh what a tangled web remains,
            When author candidly explains!

            David, pace Marmion
            http://www.quotationspage.com/quote/27150.html
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