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A139857
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Primes of the form 8x^2 + 15y^2.
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4
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23, 47, 167, 263, 383, 503, 647, 743, 863, 887, 983, 1103, 1223, 1367, 1487, 1583, 1607, 1823, 1847, 2063, 2087, 2207, 2423, 2447, 2543, 2663, 2687, 2903, 2927, 3023, 3167, 3407, 3527, 3623, 3767, 3863, 4007, 4127, 4463, 4583, 4703, 4943
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OFFSET
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1,1
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COMMENTS
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Discriminant= = -480. See A139827 for more information.
Also primes of the form 12x^2 + 12xy + 23y^2, which has discriminant = -960. - T. D. Noe, May 07 2008
Also primes of the forms 23x^2 + 22xy + 47y^2 and 23x^2 + 8xy + 32y^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 {23, 47} (mod 120).
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MATHEMATICA
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QuadPrimes2[8, 0, 15, 10000] (* see A106856 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(6000) | p mod 120 in {23, 47}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\8), w=8*x^2; for(y=1, sqrtint((lim-w)\15), if(isprime(t=w+15*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 22 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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