

A016114


Circular primes (numbers which remain prime under cyclic shifts of digits).


7



2, 3, 5, 7, 11, 13, 17, 37, 79, 113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939, 199933, 1111111111111111111, 11111111111111111111111
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OFFSET

1,1


COMMENTS

The next repunit that is prime has 317 digits, all ones. See A004023. [Harvey P. Dale, Mar 22 2012]
Only the smallest member of the cyclic shift is listed. See A068652 for all members.  Chai Wah Wu, Nov 09 2015


LINKS

Table of n, a(n) for n=1..21.
K. S. Brown, On General Palindromic Numbers
C. K. Caldwell, Circular Primes
P. De Geest, Circular Primes
H. Heinz, Prime Patterns (Illustration using 19937)


MATHEMATICA

fQ[p_] := Module[{b = IntegerDigits[p], ps}, ps = Table[FromDigits[b = RotateLeft[b]], {Length[b]}]; If[p > Min[ps], False, And @@ PrimeQ[ps]]]; Select[Prime[Range[100000]], fQ] (* T. D. Noe, Mar 22 2012 *)


CROSSREFS

Sequence includes all prime repunits (A004023). Cf. A003459.
For a sequence listing all the primeyielding cyclic permutations see A068652.
Sequence in context: A117835 A120639 A141263 * A263499 A258706 A053434
Adjacent sequences: A016111 A016112 A016113 * A016115 A016116 A016117


KEYWORD

nonn,nice,base,more


AUTHOR

Robert G. Wilson v


EXTENSIONS

One more term from Lekraj Beedassy, Nov 07 2002


STATUS

approved



