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A139649
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Primes of the form x^2 + 177*y^2.
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3
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181, 193, 241, 277, 373, 433, 577, 661, 709, 733, 757, 829, 853, 877, 997, 1069, 1201, 1237, 1549, 1597, 1609, 1621, 1657, 1669, 1693, 1777, 1789, 1933, 1993, 2113, 2269, 2293, 2377, 2389, 2557, 2617, 2677, 2749, 2833, 2857, 2917, 2953
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OFFSET
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1,1
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COMMENTS
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Discriminant = -708.
The primes are congruent to {1, 25, 49, 85, 121, 133, 145, 169, 181, 193, 205, 241, 253, 265, 277, 289, 361, 373, 433, 481, 493, 517, 529, 553, 577, 625, 661, 685, 697} (mod 708).
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LINKS
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MATHEMATICA
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QuadPrimes2[1, 0, 177, 10000] (* see A106856 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(4000) | p mod 708 in {1, 25, 49, 85, 121, 133, 145, 169, 181, 193, 205, 241, 253, 265, 277, 289, 361, 373, 433, 481, 493, 517, 529, 553, 577, 625, 661, 685, 697}]; // Vincenzo Librandi, Jul 28 2012
(Magma) k:=177; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 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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