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A102271
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Primes of the form 3x^2 + 7y^2.
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7
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3, 7, 19, 31, 103, 139, 199, 223, 271, 283, 307, 367, 439, 523, 607, 619, 643, 691, 727, 787, 811, 859, 1039, 1063, 1123, 1231, 1279, 1291, 1399, 1447, 1459, 1483, 1531, 1543, 1567, 1627, 1699, 1783, 1867, 1879, 1951, 1987, 2131, 2203, 2239
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OFFSET
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1,1
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COMMENTS
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Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = +1, chi_{-7} = -1.
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LINKS
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FORMULA
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The primes are congruent to {3, 7, 19, 31, 55} (mod 84). - T. D. Noe, May 02 2008
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MATHEMATICA
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m=3; n=7; pLst={}; lim=3000; xMax=Sqrt[lim/m]; yMax=Sqrt[lim/n]; Do[p=m*x^2+n*y^2; If[p<lim && PrimeQ[p], AppendTo[pLst, p]], {x, xMax}, {y, yMax}]; Union[pLst] (T. D. Noe, May 05 2005)
QuadPrimes2[3, 0, 7, 10000] (* see A106856 *)
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PROG
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(Magma) [p: p in PrimesUpTo(3000) | p mod 84 in [3, 7, 19, 31, 55]]; // Vincenzo Librandi, Jul 19 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\7), if(isprime(t=w+7*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 09 2017
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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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