A224322 Primes without "9" as a digit that remain prime when any single digit is replaced with "9".

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

Offset: 1

Author

Arkadiusz Wesolowski, Apr 03 2013

Keywords

• base
• more
• nonn

Comments

No more terms < 10^13.

Links

• Carlos Rivera, Puzzle 591

Crossrefs

Cf. A224319-A224321. Subsequence of A038617.

Programs

Mathematica

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
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 *)