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

```

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