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 A034813 #7 Oct 06 2019 18:19:56
%S A034813 36,74,104,132,188,222,224,305,317,344,367,368,389,457,458,475,540,
%T A034813 572,584,608,631,676,682,689,697,738,756,760,781,797,829,841,893,910,
%U A034813 911,914,928,982,1018,1104,1122,1178,1186,1317,1328,1391,1402,1406,1518
%N A034813 Concatenations C1 and C2 are both prime (see the comment lines).
%C A034813 C1 = 'prevprime(n) followed by n followed by nextprime(n)'
%C A034813 C2 = 'nextprime(n) followed by n followed by prevprime(n)'
%H A034813 Harvey P. Dale, <a href="/A034813/b034813.txt">Table of n, a(n) for n = 0..1000</a>
%e A034813 n=797 -> previous prime is 787, next prime is 809, thus '787797809' and '809797787' are both primes.
%t A034813 c1c2Q[n_]:=Module[{ia=IntegerDigits[NextPrime[n,-1]],ib=IntegerDigits[n], ic= IntegerDigits[NextPrime[n]]}, AllTrue[{FromDigits[Join[ia,ib,ic]], FromDigits[Join[ic,ib,ia]]},PrimeQ]]; Select[Range[1600],c1c2Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Apr 06 2018 *)
%Y A034813 Cf. A034808-A034821.
%K A034813 nonn,base
%O A034813 0,1
%A A034813 _Patrick De Geest_, Oct 15 1998