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A139847
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Primes of the form 6x^2 + 6xy + 19y^2.
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2
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19, 31, 139, 199, 271, 439, 619, 691, 811, 859, 1039, 1231, 1279, 1291, 1399, 1459, 1531, 1699, 1879, 1951, 2131, 2239, 2371, 2539, 2551, 2659, 2719, 2791, 2971, 3079, 3331, 3391, 3499, 3559, 3631, 3919, 4051, 4219, 4231, 4339, 4591, 4639
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OFFSET
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1,1
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COMMENTS
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Discriminant = -420. See A139827 for more information.
Also primes of the forms 19x^2 + 12xy + 24y^2 and 19x^2 + 16xy + 31y^2. See A140633. - T. D. Noe, May 19 2008
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LINKS
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FORMULA
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The primes are congruent to {19, 31, 139, 199, 271, 391} (mod 420).
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MATHEMATICA
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QuadPrimes2[6, -6, 19, 10000] (* see A106856 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(6000) | p mod 420 in {19, 31, 139, 199, 271, 391}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), s=[19, 31, 139, 199, 271, 391]); forprime(p=19, lim, if(setsearch(s, p%420), listput(v, p))); Vec(v) \\ Charles R Greathouse IV, Feb 10 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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