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Primes without "9" as a digit that remain prime when any single digit is replaced with "9".
3

%I #11 Mar 30 2015 16:46:43

%S 17,107,137,347,1013,1433,1613,3767,4337,8623,25633,31114073

%N Primes without "9" as a digit that remain prime when any single digit is replaced with "9".

%C No more terms < 10^13.

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_591.htm">Puzzle 591</a>

%t lst = {}; n = 9; Do[If[PrimeQ[p], i = IntegerDigits[p]; If[FreeQ[i, n], t = 0; s = IntegerLength[p]; Do[If[PrimeQ@FromDigits@Insert[Drop[i, {d}], n, d], t++, Break[]], {d, s}]; If[t == s, AppendTo[lst, p]]]], {p, 25633}]; lst

%t pr9Q[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,9]&&AllTrue[Table[ FromDigits[ ReplacePart[ idn,i->9]],{i,Length[idn]}],PrimeQ]]; Select[ Prime[Range[2*10^6]],pr9Q] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 30 2015 *)

%Y Cf. A224319-A224321. Subsequence of A038617.

%K base,more,nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Apr 03 2013