A224321 Primes without "7" as a digit that remain prime when any single digit is replaced with "7".

2, 3, 5, 11, 13, 19, 31, 41, 43, 61, 109, 139, 251, 643, 4933, 9433, 36493, 191416111, 1304119699

Offset: 1

Author

Arkadiusz Wesolowski, Apr 03 2013

Keywords

• base
• more
• nonn

Comments

No more terms < 10^13.

Links

• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 1304119699
• Carlos Rivera, Puzzle 591

Crossrefs

Cf. A224319-A224320, A224322. Subsequence of A038615.

Programs

Mathematica

lst = {}; n = 7; 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, 36493}]; lst
Select[Prime[Range[4000]],DigitCount[#,10,7]==0&&AllTrue[FromDigits/@Table[ReplacePart[ IntegerDigits[#],n->7],{n,IntegerLength[#]}],PrimeQ]&] (* The program generates the first 17 terms of the sequence. *) (* Harvey P. Dale, Jun 09 2024 *)