Just sent to OEIS:
1151,1193,1319,1373,1511,1733,1913,1931,1973,2003,3119,3137,3191,3371,
3559,5953,7193,7331,7793,7937,9137,9173,9311,9371,9377,10111,11113,111
19,11131,11311,11311,11551,(A086259?)

Primes such that sum of any three_neighbor_digits is prime;
first and last digits are neighbor.
Because 3-digit terms coincide with primes with prime
sum_of_digits,
it's interesting to start with 4-digit primes. All of them may
use only zero and odd digits, with the unique exclusion 2003 with one
even digit.

Now it's interesting to look for
case of prime sum_of_four_neighbor_digits (ad absurd..)
Zak

--- In primenumbers@yahoogroups.com, "Zak Seidov" <seidovzf@y...>
wrote:
> Just sent to OEIS:
>
11,23,29,41,43,47,61,67,83,89,211,2029,2111,2129,2141,2143,2161,2309,2
>
341,2383,2389,2503,2521,4111,4129,4349,4703,4943,6121,6521,6761,8329,8
>
389,8923,8929,21121,21143,21149,21211,21611,23021,23203,29201,29411,41
> 141,41143,41149,41161,41203,41411,41611,(A086244?):
>
> Primes such that a sum of any two neighbor digits is prime;
> first and last digits are neighbors.
>
> E.g. for last prime 41611: there are 5 pairs giving prime sum -
> 4+1, 1+6, 6+1, 1+1=2 (even prime!), 1+6.
>
> The number of such primes seems to be infinite(?)
> Also it's of interest to find primes with prime sums of each three
> successive digits.
>
> Zak