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 A250052 #56 Apr 03 2023 10:36:13
%S A250052 113,10103,15149,1021019,1231229,1321319,1481483,1621619,1931933,
%T A250052 1951949,3232321,7127129,7307309,7547549,29129131,71471473,100910093,
%U A250052 101410139,108910889,119411939,156415643,157315733,159715973,164516453,169816979,179117909,179217923
%N A250052 Conjoined Twin Primes: primes p such that p written in base 10 has a prefix q and a suffix r, where q and r are a pair of twin primes (in either order), and q and r overlap (i.e., strlen(q)+strlen(r)>strlen(p)).
%C A250052 The sequence is finite if the Twin Prime Conjecture is false.
%H A250052 Chris K. Caldwell, <a href="https://t5k.org/glossary/page.php?sort=TwinPrime">Twin Prime</a>
%H A250052 Rémy Sigrist, <a href="/A250052/a250052.gp.txt">PARI program for A250052</a>
%e A250052 113 is in the sequence because 113 is prime, and (11,13) is a twin prime pair, and "11" is a prefix of "113", and "13" is a suffix of "113", and the prefix and suffix overlap (i.e., strlen("11")+strlen("13")>strlen("113")).
%e A250052 3232321 is in the sequence because 3232321 is prime, and (32321,32323) is a twin prime pair, and "32323" is a prefix of "3232321", and "32321" is a suffix of "3232321", and the prefix and suffix overlap.
%o A250052 (PARI) See Links section.
%Y A250052 Cf. A001097, A001359, A006512.
%K A250052 nonn,base
%O A250052 1,1
%A A250052 _Robert C. Lyons_, Dec 07 2014
%E A250052 More terms from _Rémy Sigrist_, Aug 04 2019