PrimePi question

*To*: mathgroup at smc.vnet.net*Subject*: [mg53971] PrimePi question*From*: fartous at mail15.com*Date*: Sat, 5 Feb 2005 03:16:55 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

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