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MathGroup Archive 2003

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RE: Re: Writing a program to hunt for a prime between n^2 and (n+1)^2

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39199] RE: [mg39174] Re: Writing a program to hunt for a prime between n^2 and (n+1)^2
  • From: "Diana Mecum" <diana53 at earthlink.net>
  • Date: Mon, 3 Feb 2003 01:10:12 -0500 (EST)
  • Reply-to: <diana53 at earthlink.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Thanks Andrzej, this works great. Diana

-----Original Message-----
From: Andrzej Kozlowski [mailto:akoz at mimuw.edu.pl]
To: mathgroup at smc.vnet.net
Subject: [mg39199] Re: [mg39174] Re: Writing a program to hunt for a prime between
n^2 and (n+1)^2


One way that is at least simpler and faster then yours is just to use  
the NextPrime function in the << NumberTheory`NumberTheoryFunctions`


In[1]:=
<<NumberTheory`NumberTheoryFunctions`

In[2]:=
funct1[n_]:=NextPrime[n^2]

In[3]:=
funct1[234]

Out[3]=
54767


(Actually NextPrime is very easy to define yourself so you do not even  
need to use the package, e.g:

nextprime[n_]:=If[PrimeQ[n],n,nextprime[n+1]])


Here is a little more interesting way to get the same answer:

funct2[n_] := Prime[PrimePi[n^2] + 1]


funct2[234]


54767

This is maybe more "snazzy" but unfortunately it only works for  
relatively small n.


On Sunday, February 2, 2003, at 03:13 PM, Diana wrote:

> My program, which is not fancy:
>
> NRange = Flatten[{n, Range[10, 20, 1]}]
>
> NSquared = Flatten[NRange^2]
>
> NPlus1Squared = Flatten[(NRange+1)^2]
>
> FirstPrimeGreaterNSquared=Flatten[{"Prime>n^2",Table[NestWhile[#1+1&,n^ 
> 2,!(P
> rimeQ[#1])&],{n,10,20}]}]
>
> {NRange, NSquared, FirstPrimeGreaterNSquared, NPlus1Squared} //  
> TableForm
>
> Are there ideas to make this more snazzy, and accomplish the same  
> thing?
>
> Thanks,
>
> Diana
>
> "Diana" <diana53xiii at earthlink.remove13.net> wrote in message news:...
>> Folks,
>>
>> I am trying to come up with a snazzy way to hunt for a prime between  
>> n^2
> and
>> (n+1)^2.
>>
>> Some ideas?
>>
>> Thanks, Diana
>> --
>> =====================================================
>> "God made the integers, all else is the work of man."
>> L. Kronecker, Jahresber. DMV 2, S. 19.
>>
>>
>
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/



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