A068652 Numbers such that every cyclic permutation is a prime.

2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 197, 199, 311, 337, 373, 719, 733, 919, 971, 991, 1193, 1931, 3119, 3779, 7793, 7937, 9311, 9377, 11939, 19391, 19937, 37199, 39119, 71993, 91193, 93719, 93911, 99371, 193939, 199933, 319993

Offset

1,1

Comments

See the closely related sequence A016114 for further information. - N. J. A. Sloane, May 04 2017

These numbers are sometimes called circular primes. - Tanya Khovanova, Jul 29 2024

Links

Ray Chandler, Table of n, a(n) for n = 1..57

K. S. Brown, On General Palindromic Numbers

C. K. Caldwell, Circular Primes

Patrick De Geest, Circular Primes

H. Heinz, Prime Patterns (Illustration using 19937)

Gianni A. Sarcone, Tourbillonnants nombres premiers, Tangente Web Site, No date.

Wikipedia, Circular prime

Example

197 is a member as all the three cyclic permutations 197,971,719 are primes.

Mathematica

fQ[p_] := Module[{b = IntegerDigits[p]}, And @@ Table[PrimeQ[FromDigits[b = RotateLeft[b]]], {Length[b] - 1}]]; Select[Prime[Range[100000]], fQ] (* T. D. Noe, Mar 22 2012 *)
ecppQ[n_]:=AllTrue[FromDigits/@Table[RotateLeft[IntegerDigits[n], i], {i, IntegerLength[n]}], PrimeQ]; Select[Range[400000], ecppQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 25 2015 *)

Crossrefs

Cf. A003459, A016114, A091633.

Sequence in context: A107845 A234901 A090934 * A003459 A276132 A202264

Adjacent sequences: A068649 A068650 A068651 * A068653 A068654 A068655

Keyword

base,nonn

Author

Amarnath Murthy, Feb 28 2002

Extensions

More terms from Martin Renner, Apr 10 2002

Status

approved