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Old 2006-09-20, 17:20   #3
AntonVrba
 
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Jun 2005

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here is a base-10 evaluation of \kappa_{10} counting up to
Code:
Prime	   Actual      Calculated    Actual/Calculated
99999989     2.09217    2.07412       1.0087
999999937    2.07641    2.05933       1.0083
9999999967   2.06389    2.00702       1.0078   
99999999977  2.05366    2.03844       1.00747
Actual cumulative digit count of all primes 2 to p divided by the last prime p (C program)

Calculated value \frac{\pi(p)\, c_{10}(p)}{p^2}

\pi(p) being the prime counting function

An on the same basis a base-2 evaluation for \kappa_2

Code:
32749     0.845614   0.804225   1.05146
65521     0.837533   0.798769   1.04853
131071    0.832198   0.794553   1.04738
262139    0.825139   0.789684   1.0449
524287    0.820511   0.78624   1.04359
1048573   0.815104   0.782262   1.04198
2097143   0.810823   0.779118   1.04069
4194301   0.806539   0.776155   1.03915
8388593   0.802665   0.773417   1.03782
16777213   0.798989   0.770954   1.03636
33554393   0.795861   0.768785   1.03522
67108859   0.792815   0.766688   1.03408
134217689   0.790022   0.764787   1.033
268435399   0.787444   0.763058   1.03196
536870909   0.785043   0.76144   1.031
1073741789   0.782845   0.75996   1.03011
2147483647   0.780761   0.758568   1.02926

Last fiddled with by AntonVrba on 2006-09-20 at 18:11
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