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 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 (list; graph; refs; listen; history; text; internal format)
 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 K. S. Brown, On General Palindromic Numbers C. K. Caldwell, Circular Primes P. De Geest, Circular Primes 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 prime-yielding 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 EXTENSIONS One more term from Lekraj Beedassy, Nov 07 2002 STATUS approved

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