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A168147
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Primes of the form 10*n^3 + 1.
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15
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11, 271, 641, 2161, 33751, 40961, 58321, 138241, 196831, 270001, 297911, 466561, 506531, 795071, 1326511, 1406081, 1851931, 2160001, 3890171, 4218751, 5314411, 5513681, 6585031, 7290001, 8043571, 11910161, 12597121, 12950291, 14815441
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OFFSET
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1,1
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COMMENTS
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(1) These primes all with end digit 1=1^3 are concatenations of two CUBIC numbers: "n^3 1".
(2) It is conjectured that the sequence is infinite.
(3) It is an open problem if 3 consecutive naturals n exist which give such a prime.
No three such integers exist, as every n = 2 (mod 3) yields 10n^3 + 1 = 0 (mod 3). - Charles R Greathouse IV, Apr 24 2010
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REFERENCES
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Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
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LINKS
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FORMULA
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MATHEMATICA
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PROG
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(PARI) for(n=1, 2e2, isprime(n^3*10+1) && print1(n^3*10+1", ")) \\ M. F. Hasler, Jul 24 2011
(Magma) [ a: n in [1..150] | IsPrime(a) where a is 10*n^3+1 ]; // Vincenzo Librandi, Jul 25 2011
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CROSSREFS
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Cf. A030430 (primes of the form 10*n+1).
Cf. A167535 (concatenation of two square numbers which give a prime).
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KEYWORD
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nonn,base,easy
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AUTHOR
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Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 19 2009
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STATUS
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approved
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