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A102273
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Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = -1, chi_{-7} = +1.
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8
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11, 23, 71, 107, 179, 191, 239, 263, 347, 359, 431, 443, 491, 599, 659, 683, 743, 827, 863, 911, 947, 1019, 1031, 1103, 1163, 1187, 1283, 1367, 1439, 1451, 1499, 1523, 1583, 1607, 1619, 1667, 1787, 1871, 2003, 2027, 2039, 2087
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OFFSET
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1,1
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COMMENTS
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The 2-class number of these fields is always 4.
Primes of the form 2x^2 - 2xy + 11y^2 with x nonnegative and y positive. - T. D. Noe, May 08 2005
Also primes of the forms 8x^2 + 4xy + 11y^2 and 11x^2 + 2xy + 23y^2. See A140633. - T. D. Noe, May 19 2008
The discriminant of positive definite binary quadratic form (2,2,11) is -84. - Hugo Pfoertner, Jul 14 2019
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LINKS
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FORMULA
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The primes are congruent to {2, 11, 23, 71} (mod 84). - T. D. Noe, May 02 2008
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MATHEMATICA
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f[x_, y_]:=2*x^2+2*x*y+11*y^2; lst={}; Do[Do[p=f[x, y]; If[PrimeQ[p], AppendTo[lst, p]], {y, -5!, 6!}], {x, -5!, 6!}]; Take[Union[lst], 5! ] (* Vladimir Joseph Stephan Orlovsky, Jul 06 2009 *)
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PROG
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(Magma) [p: p in PrimesUpTo(3000) | p mod 84 in [2, 11, 23, 71]]; // Vincenzo Librandi, Jul 19 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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