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A030469
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Primes which are concatenations of three consecutive primes.
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17
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5711, 111317, 171923, 313741, 414347, 8997101, 229233239, 239241251, 263269271, 307311313, 313317331, 317331337, 353359367, 359367373, 383389397, 389397401, 401409419, 409419421, 439443449, 449457461
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OFFSET
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1,1
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COMMENTS
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a(n) = "p(k) p(k+1) p(k+2)" where p(k) is k-th prime
It is conjectured that sequence is infinite. - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
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REFERENCES
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Richard E. Crandall, Carl Pomerance: Prime Numbers, Springer 2005 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
John Derbyshire: Prime obsession, Joseph Henry Press, Washington, DC 2003 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009
Marcus du Sautoy: Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004
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LINKS
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FORMULA
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EXAMPLE
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(1) 5=p(3), 7=p(4), 11=p(5) gives a(1).
(2) 7=p(4), 11=p(5), 13=p(6), but 71113 = 7 x 10159
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MATHEMATICA
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Select[Table[FromDigits[Flatten[IntegerDigits/@{Prime[n], Prime[n+1], Prime[n+2]}]], {n, 11000}], PrimeQ] (* Zak Seidov, Oct 16 2009 *)
concat[{a_, b_, c_}]:=FromDigits[Flatten[IntegerDigits/@{a, b, c}]]; Select[ concat/@ Partition[ Prime[ Range[200]], 3, 1], PrimeQ] (* Harvey P. Dale, Sep 06 2017 *)
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PROG
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(PARI) for(i=1, 999, isprime(p=eval(Str(prime(i), prime(i+1), prime(i+2)))) & print1(p, " ")) \\ M. F. Hasler, Nov 10 2009
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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