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Re: goldbach prime partitions for arbitrary integer n => 4

• To: mathgroup at smc.vnet.net
• Subject: [mg43018] Re: [mg42986] goldbach prime partitions for arbitrary integer n => 4
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Fri, 8 Aug 2003 00:26:31 -0400 (EDT)
• References: <200308070453.AAA24088@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Re: goldbach prime partitions for arbitrary integer n => 4
    • From: Dr Bob <drbob@bigfoot.com>

• References:
  • goldbach prime partitions for arbitrary integer n => 4
    • From: gilmar.rodriguez@nwfwmd.state.fl.us (Gilmar Rodríguez Pierluissi)