

A016114


Circular primes (numbers that 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
It is highly likely that all circular primes not on the list above are repunits (see Caldwell link).  Ray Chandler, May 04 2017


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)
Gianni Sarcone, Tourbillonnants nombres premiers, Tangente Web Site, No date. The claim stated here is false (see comments in A068652).


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 A265408
Adjacent sequences: A016111 A016112 A016113 * A016115 A016116 A016117


KEYWORD

nonn,nice,base


AUTHOR

Robert G. Wilson v


EXTENSIONS

One more term from Lekraj Beedassy, Nov 07 2002


STATUS

approved



