## Re: 2 > exp(Euler)

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• ... 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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>
> 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
• ... 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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"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
• ... 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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>
> 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
• ... 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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