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A139861
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Primes of the form 2x^2 + 65y^2.
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2
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2, 67, 73, 83, 97, 137, 163, 193, 227, 307, 353, 457, 577, 587, 593, 617, 643, 683, 787, 827, 947, 977, 1033, 1097, 1123, 1163, 1217, 1307, 1523, 1553, 1627, 1657, 1697, 1723, 1747, 1753, 1787, 1867, 1913, 1987, 2017, 2113, 2137, 2153, 2203
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OFFSET
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1,1
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COMMENTS
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Discriminant = -520. See A139827 for more information.
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LINKS
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FORMULA
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The primes are congruent to {2, 33, 57, 67, 73, 83, 97, 123, 137, 163, 177, 187, 193, 203, 227, 267, 297, 307, 323, 353, 427, 457, 473, 483, 513} (mod 520).
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MATHEMATICA
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QuadPrimes2[2, 0, 65, 10000] (* see A106856 *)
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PROG
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(Magma) [ p: p in PrimesUpTo(3000) | p mod 520 in {2, 33, 57, 67, 73, 83, 97, 123, 137, 163, 177, 187, 193, 203, 227, 267, 297, 307, 323, 353, 427, 457, 473, 483, 513}]; // Vincenzo Librandi, Jul 29 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\65), if(isprime(t=w+65*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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