Re: goldbach prime partitions for arbitrary integer n => 4
- To: mathgroup at smc.vnet.net
- Subject: [mg43012] Re: goldbach prime partitions for arbitrary integer n => 4
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Fri, 8 Aug 2003 00:26:26 -0400 (EDT)
- Organization: The University of Western Australia
- References: <bgsn4c$nnq$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bgsn4c$nnq$1 at smc.vnet.net>,
gilmar.rodriguez at nwfwmd.state.fl.us (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!
Although others will probably provide more efficient (and general)
solutions, here is one way to generate the solutions you are after:
PrimePair[n_Integer] := Select[Table[Prime[i], {i, PrimePi[n/2]}],
PrimeQ[n - #] & ] /. p_ :> {p, n - p}
PrimePair[200]
Cheers,
Paul
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