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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=



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