%I A037053
%S A037053 101,1009,10007,100003,1000003,20000003,100000007,1000000007,
%T A037053 30000000001,100000000003,2000000000003,40000000000001,1000000000000037,
%U A037053 6000000000000001,20000000000000003,100000000000000003
%N A037053 Smallest prime containing exactly n 0's.
%C A037053 Notice that certain entries require n+3 digits such as a(13). Those which 
               do not require three digits besides n zeros are in A085824. Conjecture, 
               a prime of this form, A037053, requires at most three judiciously 
               placed digits, two on the exterior and one inside. - Robert G. Wilson 
               v.
%t A037053 a[n_List] := Join[{x}, n, {y}]; f[n_] := Block[{p = Join[{x}, Table[ 
               0, {i, 1, n}], {y}], c = Table[j, {j, 1, 9}], q = {}}, Do[q = Append[q, 
               Replace[p, {x -> c[[i]], y -> c[[j]]}, 2]], {i, 1, 9}, {j, 1, 9}]; 
               r = Min[ Select[ FromDigits /@ q, PrimeQ[ # ] & ]]; If[r != Infinity, 
               r, p = Permutations[ Join[ Table[0, {i, 1, n}], {d}]]; p = Map[a, 
               p]; q = {}; Do[q = Append[q, Replace[p, {d -> c[[i]], x -> c[[j]], 
               y -> c[[k]]}, 2]], {i, 1, 9}, {j, 1, 9}, {k, 1, 9}]; Min[ Select[
%Y A037053 Cf. A037052, A034388, A085824, A036507-A036536.
%Y A037053 Cf. A037055, A037057, A037059, A037061, A037063, A037065, A037067.
%Y A037053 Sequence in context: A164842 A082276 A069597 this_sequence A139535 A139536 
               A115820
%Y A037053 Adjacent sequences: A037050 A037051 A037052 this_sequence A037054 A037055 
               A037056
%K A037053 nonn,base
%O A037053 1,1
%A A037053 Patrick De Geest (pdg(AT)worldofnumbers.com), Jan 04 1999.
%E A037053 More terms from Victoria A Sapko (vsapko(AT)canes.gsw.edu), Aug 16 2002
%E A037053 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 04 2003
%E A037053 Jul 09 2003: Zakir Seidov comments that the Mathematica program is incorrect. 
               The sequence should be recheked.