Re: Re: goldbach prime partitions for arbitrary integer n => 4
- To: mathgroup at smc.vnet.net
- Subject: [mg43032] Re: [mg43018] Re: [mg42986] goldbach prime partitions for arbitrary integer n => 4
- From: Dr Bob <drbob at bigfoot.com>
- Date: Sat, 9 Aug 2003 02:57:34 -0400 (EDT)
- References: <200308070453.AAA24088@smc.vnet.net> <200308080426.AAA05617@smc.vnet.net>
- Reply-to: drbob at bigfoot.com
- Sender: owner-wri-mathgroup at wolfram.com
And, to put it in the same form as other solutions:
Developer`SetSystemOptions["ReduceOptions" -> {"DiscreteSolutionBound" ->
100}];
Reduce[Join[eqn, constraints], {p, q}]
{p, q} /. List[ToRules@%]
Bobby
On Fri, 8 Aug 2003 00:26:31 -0400 (EDT), Daniel Lichtblau
<danl at wolfram.com> wrote:
> Gilmar Rodríguez Pierluissi wrote:
>>
>> If one wishes to compute:
>> eqn={p+q==200}; constraints={2<=p<=100, p<=q, p,q \[Element]Primes};
>> wouldn't it be nice that if you evaluate:
>> Solve[eqn,constraints,{p,q}]
>> you would get:
>> {{97,103},{73,127},{61,139},{43,157},{37,163},{19,181},{7,193},{3,197}}
>> ?
>> A module (or program) that could solve:
>> eqn={p+q==n}; constraints={2<=p<=n/2, p<=q, p,q \[Element]Primes};
>> Solve[eqn,constraints,{p,q}]
>> for a specified n, (n=>4, n \[Element]Integer), would be even better!
>> Thank you!
>
> You can use Reduce in version 5.
>
> eqn = {p+q==200};
> constraints = {2<=p<=100, p<=q, Element[{p,q},Primes]};
>
> InputForm[Reduce[Join[eqn,constraints], {p,q}]]
> Out[3]//InputForm= (p | q) \[Element] Primes && C[1] \[Element] Integers
> && Inequality[2, LessEqual, C[1], LessEqual, 100] && p == C[1] && q ==
> 200 - C[1]
>
> The trick is to realize that there is a relatively low bound on how many
> discrete solutions are allowed by default (it is 10). If you do
>
> Developer`SetSystemOptions["ReduceOptions" ->
> {"DiscreteSolutionBound" ->100}];
>
> then we get something more along the lines desired.
>
> InputForm[Reduce[Join[eqn,constraints], {p,q}]]
> Out[5]//InputForm= (p == 3 && q == 197) || (p == 7 && q == 193) || (p ==
> 19 && q == 181) || (p == 37 && q == 163) || (p == 43 && q == 157) || (p
> == 61 && q == 139)
> || (p == 73 && q == 127) || (p == 97 && q == 103)
>
>
> Daniel lichtblau
> Wolfram Research
>
>
--
majort at cox-internet.com
Bobby R. Treat
- References:
- goldbach prime partitions for arbitrary integer n => 4
- From: gilmar.rodriguez@nwfwmd.state.fl.us (Gilmar Rodríguez Pierluissi)
- Re: goldbach prime partitions for arbitrary integer n => 4
- From: Daniel Lichtblau <danl@wolfram.com>
- goldbach prime partitions for arbitrary integer n => 4