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)).

113, 10103, 15149, 1021019, 1231229, 1321319, 1481483, 1621619, 1931933, 1951949, 3232321, 7127129, 7307309, 7547549, 29129131, 71471473, 100910093, 101410139, 108910889, 119411939, 156415643, 157315733, 159715973, 164516453, 169816979, 179117909, 179217923

Offset: 1

Author

Robert C. Lyons, Dec 07 2014

Keywords

• nonn
• base

Comments

The sequence is finite if the Twin Prime Conjecture is false.

Examples

			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")).
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.
		

Links

• Chris K. Caldwell, Twin Prime
• Rémy Sigrist, PARI program for A250052

Crossrefs

Cf. A001097, A001359, A006512.

Programs

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, Aug 04 2019