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A139865
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Primes of the form 7x^2 + 19y^2.
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1
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7, 19, 47, 83, 131, 139, 199, 251, 271, 283, 311, 367, 419, 467, 479, 503, 587, 619, 643, 647, 691, 719, 727, 859, 1151, 1223, 1259, 1279, 1483, 1487, 1531, 1543, 1559, 1567, 1783, 1811, 1847, 1867, 1879, 1907, 1987, 2063, 2099, 2239, 2243, 2267
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OFFSET
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1,1
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COMMENTS
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Discriminant=-532. See A139827 for more information.
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LINKS
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FORMULA
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The primes are congruent to {7, 19, 47, 55, 83, 87, 111, 115, 131, 139, 159, 187, 195, 199, 215, 251, 271, 283, 311, 327, 339, 367, 391, 419, 423, 467, 479, 495, 503} (mod 532).
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MATHEMATICA
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QuadPrimes2[7, 0, 19, 10000] (* see A106856 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(3000) | p mod 532 in {7, 19, 47, 55, 83, 87, 111, 115, 131, 139, 159, 187, 195, 199, 215, 251, 271, 283, 311, 327, 339, 367, 391, 419, 423, 467, 479, 495, 503}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=0, sqrtint(lim\7), w=7*x^2; for(y=0, sqrtint((lim-w)\19), if(isprime(t=w+19*y^2), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Mar 07 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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