Re: Prime count question

*To*: mathgroup at smc.vnet.net*Subject*: [mg126488] Re: Prime count question*From*: Andrzej Kozlowski <akozlowski at gmail.com>*Date*: Mon, 14 May 2012 01:35:49 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201205130702.DAA16830@smc.vnet.net>

On 13 May 2012, at 09:02, J.Jack.J. wrote: > Let pi(x) be the number of primes greater than or equal to x. This "number" is infinity for every finite x=E2=80=A6??? If you mean less or equal than it is implemented in Mathematica as the function PrimePi > > Then how do I find, through Mathematica, x such that > > t(x) = pi(x) / ((x/ln(x))*(1+1/ln(x) + 2.51/(ln^2(x)))) > > is the highest t(y) such that 599 <= y <= 355991? > > Many thanks in advance -- thanks also to those who helped with my > previous question. > t[x_] := PrimePi[x]/(x/Log[x] + (1 + 1/Log[x] + 2.51/Log[x]^2)) Maximize[{t[x], 599 <= x <= 355991}, x] {1.15703, {x -> 607.004}} Andrzej Koz=C5=82owski=

**References**:**Prime count question***From:*"J.Jack.J." <jack.j.jepper@googlemail.com>