%I
%S 1,2,3,5,7,11,13,17,23,31,37,53,71,73,113,131,137,173,311,313,317,373,
%T 1373,3137
%N Noncomposite numbers in which every substring is noncomposite.
%C It is easy to see that this sequence is complete  the only potential 5digit candidate 31373 is not prime.  _Tanya Khovanova_, Dec 09 2006
%e 137 is a member as all the substrings, i.e. 1, 3, 7, 13, 37, 137, are noncomposite.
%e All substrings of 3137 are noncomposite numbers: 1, 3, 7, 13, 37, 137, 313, 3137.  _Jaroslav Krizek_, Dec 25 2011
%t noncompositeQ[n_] := n == 1  PrimeQ[n]; Reap[ Do[ id = IntegerDigits[n]; lid = Length[id]; test = And @@ noncompositeQ /@ FromDigits[#, 10]& /@ Flatten[ Table[ Take[id, {i, j}], {i, 1, lid}, {j, i, lid}], 1]; If[test, Sow[n]], {n, Join[{1}, Prime /@ Range[10000]]}]][[2, 1]](* _JeanFrançois Alcover_, May 09 2012 *)
%Y Cf. A012884, A062115, A202262.
%K base,nonn,fini,full
%O 1,2
%A _Amarnath Murthy_, Mar 02 2002
%E 1 added following a redefinition by _Jaroslav Krizek_.  _R. J. Mathar_, Jan 20 2012
