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

Author

Amarnath Murthy, Feb 28 2002

Keywords

• base
• nonn

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

Examples

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

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

Crossrefs

Cf. A003459, A016114, A091633.

Programs

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 *)

Extensions

More terms from Martin Renner, Apr 10 2002