A225421 Prime numbers consisting of only odd digits such that there is only one permutation of its digits that produces a prime number.

3, 5, 7, 11, 19, 53, 59, 151, 353, 557, 599, 773, 997, 5557, 7559, 11119, 15559, 59999, 71777, 75553, 79999, 99991, 191999, 511111, 555557, 575557, 775777, 777977, 799979, 1111151, 3353333, 5595559, 5755559, 7577777, 9999991, 33335333, 55555553, 55555559

Offset: 1

Author

T. D. Noe, May 07 2013

Keywords

• nonn
• base

Crossrefs

Cf. A039986 (similar, but allowing even digits also).

Programs

Mathematica

t2 = Select[Prime[Range[100000]], Intersection[{0, 2, 4, 6, 8}, Union[IntegerDigits[#]]] == {} &]; t = {}; Do[If[Length[Select[Table[FromDigits[k], {k, Permutations[IntegerDigits[p]]}], PrimeQ]] == 1, AppendTo[t, p]], {p, t2}]; t
edpQ[n_]:=Module[{idn=IntegerDigits[n]},AllTrue[idn,OddQ]&&Count[ FromDigits/@ Permutations[idn],?PrimeQ]==1]; Select[Prime[ Range[ 332*10^4]],edpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale, Nov 25 2018 *)