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A139874
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Primes of the form 3x^2 + 56y^2.
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3
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3, 59, 83, 131, 227, 251, 419, 467, 563, 587, 971, 1091, 1259, 1307, 1427, 1571, 1811, 1907, 1931, 1979, 2099, 2243, 2267, 2411, 2579, 2819, 2939, 3083, 3251, 3323, 3491, 3659, 3779, 3923, 3947, 4091, 4259, 4283, 4451, 4787, 4931, 5003
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OFFSET
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1,1
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COMMENTS
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Discriminant = -672. See A139827 for more information.
Except for 3, also primes of the form 20x^2 + 12xy + 27y^2. See A140633. - T. D. Noe, May 19 2008
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LINKS
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FORMULA
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Except for 3, the primes are congruent to {59, 83, 131} (mod 168).
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MATHEMATICA
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QuadPrimes2[3, 0, 56, 10000] (* see A106856 *)
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PROG
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(Magma) [3] cat [ p: p in PrimesUpTo(6000) | p mod 168 in {59, 83, 131}]; // Vincenzo Librandi, Jul 30 2012
(PARI) list(lim)=my(v=List(), w, t); for(x=1, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\56), if(isprime(t=w+56*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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