MathGroup Archive 2005

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PrimePi question


we know that to approximate the number of primes less than number n we have many 
approximate methods such as the old one n/ln(n)
but there are no exact solution, however the PrimePi function are giving exact 
answer in a reasonable time, i have found in my celeron 2GHz that the number of 
primes less than a One Tera:
In:= Timing[PrimePi[1000000000000]]
Out= {8.84 Seconds, 37607912018}

Does wolfram have a top secret formula ?? or it is a recent formula discovery.
jack


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