Mike McCarty wrote: > Brian Beesley wrote: > >> On Sunday 01 October 2006 18:28, Soo Reams wrote: >>> Not certain of this, but I think Pi(x) is defined as the number of >>> primes less than or equal to x. The Riemann hypothesis is concerned with >>> a particular approximation to Pi(x), a more accurate one than Pi(x) = x >>> / lg x. >>> >> Isn't it _perfectly_ accurate _unless_ RH is _false_? >> > > Absolutely not. Even if RH is true, it is not perfectly accurate. > > Pi(18) = 7 > > 18/ln(18) ~ 6.23 > > 18/lg(18) ~ 4.3 > > Pi(19) = 8 > > 19/ln(19) ~ 6.45 > > So it is not even "chose closest integer". > > (lg x often means log base 2 of x) > > Mike > Err, I'm pretty sure Brian meant that the Riemann zeta approximation is perfect, not the x/ln x one.
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