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A033207
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Primes of the form x^2 + 7*y^2.
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7
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7, 11, 23, 29, 37, 43, 53, 67, 71, 79, 107, 109, 113, 127, 137, 149, 151, 163, 179, 191, 193, 197, 211, 233, 239, 263, 277, 281, 317, 331, 337, 347, 359, 373, 379, 389, 401, 421, 431, 443, 449, 457, 463, 487, 491
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OFFSET
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1,1
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COMMENTS
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Except for a(1) = 7, these are the primes which can be written in the form a^2 + 7*b^2 with a > 0 and b > 0. - V. Raman, Sep 08 2012
These are the primes p for which p^3 - 1 is divisible by 7, with two exceptions: p = 2 is not in the sequence even though 2^3 - 1 is divisible by 7, and p = 7 is in the sequence even though 7^3 - 1 is not divisible by 7. Except for p = 7, if p^3 - 1 is not divisible by 7, it is congruent to 5 (mod 7). - Richard R. Forberg, Jun 03 2013
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REFERENCES
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David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.
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LINKS
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FORMULA
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Primes congruent to {1, 7, 9, 11, 15, 23, 25} (mod 28). - T. D. Noe, Apr 29 2008
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MATHEMATICA
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QuadPrimes2[1, 0, 7, 10000] (* see A106856 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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