A077361 Smallest n-digit prime whose external digits as well as internal digits form a prime, or 0 if no such number exists.

0, 0, 127, 1021, 10037, 100057, 1000033, 10000079, 100000037, 1000000021, 10000000033, 100000000057, 1000000000039, 10000000000037, 100000000000031, 1000000000000037, 10000000000000079, 100000000000000021

Offset: 0

Author

Amarnath Murthy, Nov 05 2002

Keywords

• base
• hard
• nonn

Comments

Conjecture: no entry is zero for n>2.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A069686, A077359, A077360, A077362.

Programs

Mathematica

eifpQ[n_]:=Module[{idn=IntegerDigits[n]},PrimeQ[FromDigits[{First[ idn], Last[ idn]}]]&&PrimeQ[FromDigits[Rest[Most[idn]]]]]; ndp[pwr_]: = Module[ {p=NextPrime[10^pwr]},While[!eifpQ[p],p=NextPrime[p]];p]; Join[ {0,0}, Table[ndp[i],{i,2,20}]] (* Harvey P. Dale, Jan 03 2015 *)

Extensions

More terms from Sascha Kurz, Jan 11 2003