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A016114
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Circular primes (numbers that remain prime under cyclic shifts of digits).
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9
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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
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1,1
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COMMENTS
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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
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LINKS
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MATHEMATICA
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circularPrimeQ[p_] := Module[{d = IntegerDigits[p], ps}, ps = Table[FromDigits[d = RotateLeft[d]], {Length[d]}]; If[p > Min[ps], False, And @@ PrimeQ[ps]]]; Select[Prime[Range[100000]], circularPrimeQ] (* T. D. Noe, Mar 22 2012 *)
Union[Select[Union/@((FromDigits/@Table[RotateRight[IntegerDigits[#], n], {n, IntegerLength[ #]}])&/@Prime[Range[20000]]), AllTrue[#, PrimeQ]&]][[All, 1]] (* The program generates the first 19 terms of the sequence. *) (* Harvey P. Dale, Nov 14 2022 *)
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CROSSREFS
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For a sequence listing all the prime-yielding cyclic permutations see A068652.
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KEYWORD
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nonn,nice,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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