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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*: [mg39183] Re: [mg39174] Re: Writing a program to hunt for a prime between n^2 and (n+1)^2
*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>
*Date*: Mon, 3 Feb 2003 01:08:18 -0500 (EST)
*Sender*: owner-wri-mathgroup at wolfram.com
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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