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A033205
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Primes of form x^2 + 5*y^2.
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24
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5, 29, 41, 61, 89, 101, 109, 149, 181, 229, 241, 269, 281, 349, 389, 401, 409, 421, 449, 461, 509, 521, 541, 569, 601, 641, 661, 701, 709, 761, 769, 809, 821, 829, 881, 929, 941, 1009, 1021, 1049, 1061, 1069, 1109, 1129, 1181, 1201, 1229, 1249, 1289, 1301, 1321, 1361, 1381, 1409, 1429, 1481, 1489
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OFFSET
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1,1
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COMMENTS
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It is a classical result that p is of the form x^2 + 5y^2 if and only if p = 5 or p == 1 or 9 mod 20 (see Cox, page 33). - N. J. A. Sloane, Sep 20 2012
Except for 5, also primes of the form x^2 + 25y^2. See A140633. - T. D. Noe, May 19 2008
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REFERENCES
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David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989; see p. 33.
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LINKS
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FORMULA
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MATHEMATICA
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QuadPrimes2[1, 0, 5, 10000] (* see A106856 *)
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PROG
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(Magma) [p: p in PrimesUpTo(2000) | NormEquation(5, p) eq true]; // Bruno Berselli, Jul 03 2016
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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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