PI(N) = N /{A * LOG(N)^2 +B * LOG(N) + C}. Note: LOG(N) is the common log.(adsbygoogle = window.adsbygoogle || []).push({});

This formula works for N up to 10^23. The accuracy depends on the number of digits

after the decimal point in the coefficients A, B & C. I used a Lotus123 spreadsheet to

calculate them. My calculated values are;

A = -0.000223480708389211732

B = 2.31221822291801513

C = -1.12554500288863357

The correct value of PI(10^23) = 1,925,320,391,606,803,968,923. The calculated value is

1,925,400,258,044,147,870,000

Not exact, but within .005%

I think that better approximations could be attained if the accuracy of the coefficients was

increased. But I have no way of testing this hypothesis

Bill J

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# Prime Number Counting

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