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Re: Prime count question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg126485] Re: Prime count question
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Mon, 14 May 2012 01:34:47 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201205130702.DAA16830@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

Here are the k largest t@x, where k = 5:

Clear[t]
t[x_] := Evaluate@
   Rationalize[PrimePi@x / ((x/Log@x)*(1 + 1/Log@x + 2.51/(Log@x)^2))]
k = 5;
pairs = Table[{N[t@x - 1] + 1, x}, {x, 599, 355991}];
pairs[[Ordering[pairs, -k]]]

{{1.00018, 59754}, {1.00018, 59798}, {1.00018, 59809}, {1.00019,
   59753}, {1.00019, 59797}}

Bobby

On Sun, 13 May 2012 02:02:40 -0500, J.Jack.J.  
<jack.j.jepper at googlemail.com> wrote:

> Let pi(x) be the number of primes greater than or equal to x.
>
> 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.
>


-- 
DrMajorBob at yahoo.com



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