A224320 Primes without "3" as a digit that remain prime when any single digit is replaced with "3".

2, 5, 7, 11, 17, 41, 47, 71, 107, 167, 179, 197, 449, 859, 1019, 1061, 1499, 2089, 16901, 47717, 56269, 86269, 11917049

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-A224322. Subsequence of A038611.

Programs

Mathematica

lst = {}; n = 3; 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, 86269}]; lst
p3Q[n_]:=Module[{idn=IntegerDigits[n]},FreeQ[idn,3] && AllTrue[ FromDigits/@ Table[ReplacePart[idn,i->3],{i,IntegerLength[n]}],PrimeQ]]; Select[Prime[Range[10^6]],p3Q] (* The program uses the function AllTrue from Mathematica version 10 *) (* Harvey P. Dale, Aug 20 2014 *)