FindInstance for sum of primes
- To: mathgroup at smc.vnet.net
- Subject: [mg115478] FindInstance for sum of primes
- From: leigh pascoe <leigh at evry.inserm.fr>
- Date: Tue, 11 Jan 2011 19:25:14 -0500 (EST)
Dear Mathgroup,
2011 is the sum of 11 consecutive primes. I want to check if any other
years have a similar property.
Now define
f[n_, m_] := Sum[Prime[i], {i, n, n + m}];
eq = Mod[f[n, m] - year, 1000] == 0
and we see that
In[64]:= Mod[f[37, 10] - 2011, 1000]
Out[64]= 0
but
In[65]:= FindInstance[eq, {n, m, year}, Integers]
During evaluation of In[65]:= FindInstance::exvar: The system contains a
nonconstant expression i independent of variables {n,m,year}. >>
Out[65]= FindInstance[Mod[-year + \!\(\*UnderoverscriptBox[\(\[Sum]\),
\(i = n\), \(m + n\)]\(Prime[i]\)\), 1000] == 0, {n, m, year}, Integers]
Apparently FindInstance doesn't like the dummy variable "i". How can we
perform this search in Mathematica??
LP