Re: Percentage of Primes

*To*: mathgroup at smc.vnet.net*Subject*: [mg128193] Re: Percentage of Primes*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Sun, 23 Sep 2012 02:59:13 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20120922064747.0DFD4685F@smc.vnet.net>

On Sep 22, 2012, at 2:47 AM, Jared E <eggers.jared at gmail.com> wrote: > I'm brand new to Mathematica, so there's only so much I can teach myself by playing around with it. Could somebody give me some sample code for displaying a graph of the percentage of primes from, say, 1 to 1000. The x-axis would be the integers from 1 to 1000 and the y-axis would indicate the density of primes from 1 to n. I can then figure out how to apply this code to other types of problems. Really easy, since Mathematica already the built-in function PrimePi: PrimePi[n] is the number of primes less than or equal to n. ListPlot[Table[PrimePi[n]/n, {n, 1, 1000, 1}]] (That calculates and plots the ratios as decimal fractions; of course just multiply by 100 for percentage.) Explanation: PrimePi[12] 5 Table[PrimePi[n]/n, {n, 1, 12, 1}] {0, 1/2, 2/3, 1/2, 3/5, 1/2, 4/7, 1/2, 4/9, 2/5, 5/11, 5/12} --- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Percentage of Primes***From:*Jared E <eggers.jared@gmail.com>