--- 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