This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A211686 #16 May 11 2018 14:18:27
%S A211686 11093,11171,11933,12011,12239,12377,12791,12917,13037,13217,13613,
%T A211686 14519,14591,14813,14831,15233,15791,16073,16091,16217,16673,16691,
%U A211686 17333,17417,17477,18233,18311,18713,18719,18731,19013,19319,19739,19973,21319
%N A211686 Prime numbers > 10000 such that all the substrings of length >= 4 are primes (substrings with leading '0' are considered to be nonprime).
%C A211686 Only numbers > 10000 are considered, since all 4-digit primes are trivial members.
%C A211686 By definition, each term of the sequence with more than 5 digits is built up by an overlapped union of previous terms, i.e., a(254)=182339 has the two embedded previous terms a(26)=18233 and a(208)=82339.
%C A211686 The sequence is finite, the last term is 934919 (n=263). Proof of finiteness: Let p be a number with more than 6 digits. By the argument above, each 6-digit substring must be a previous term. The only 6-digit terms are 182339, 349199, 432713, 487793, 511933, 654799, 782339, 787793, 917333, 934919 (n=254..263, see b-file). As can be directly verified, none of them can be extended to a 7-digit number with the desired property.
%H A211686 Hieronymus Fischer, <a href="/A211686/b211686.txt">Table of n, a(n) for n = 1..263</a>
%e A211686 a(1)=11093, since all substrings of length >= 4 are primes (1109, 1093, and 11093).
%e A211686 a(263)=934919, all substrings of length >= 4 (9349, 3491, 4919, 93491, 34919 and 934919) are primes.
%t A211686 sspQ[n_]:=Module[{idn=IntegerDigits[n],s1,s2},s1=FromDigits[Most[idn]];s2=FromDigits[Rest[idn]];IntegerLength[s1]==IntegerLength[s2]==4 && AllTrue[{s1,s2},PrimeQ]]; Select[Prime[Range[1230,9592]],sspQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* The program generates all 253 five-digit terms of the sequence *)(* _Harvey P. Dale_, May 11 2018 *)
%Y A211686 Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682, A211684, A211685.
%K A211686 nonn,fini,base
%O A211686 1,1
%A A211686 _Hieronymus Fischer_, Jun 08 2012