Someone named '**Dale**' submitted the following
curio to the well know Prime
Curios! pages:

**18731 is the smallest prime
which is the average of both its immediate and second neighbors**

That is to say, **18731**,
is at the 'center' of the following symmetrically spaced consecutive primes:

**18713,
18719, ****18731****,
18743, 18749**

such that 18731 = (18719+18743)/2=(18713+18749)/2

I have generalized this and ask for the earliest prime
such that it is the average of its k-th immediate consecutive prime
neighbors, for k=1 to m, for m=1, 2, 3, .... The **Dale**'s example is
the solution for m=2.

The sequence of these earlier primes goes like this:
5, 18731, 683783, 98303927, ... (?)

**Question: Find more terms to
this sequence.**

**Solution:**

**Faride Firoozbakht** and **J. K. Andersen**
found that the 5th term of this sequence was already discovered by Jud
McCranie and reported in the EIS sequence A055380.

So the first real unknown term is the 6th one.

***

**Giovanni Resta** found it! (October, 2004):

...the next one (sixth of the sequence) is centered in 1169769749219
and the gaps are (single, cumulative): 6, 60, 12, 12, 6, 12, 12, 6, 12,
12, 60, 6 -108, -102, -42, -30, -18, -12, 0, 12, 18, 30, 42, 102, 108 so
the constellation is:

1169769749327

1169769749321

1169769749261

1169769749249

1169769749237

1169769749231

1169769749219 <- center

1169769749207

1169769749201

1169769749189

1169769749177

1169769749117

1169769749111

***