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Primes of the form 2x^2 + 27y^2.
2

%I #19 Feb 09 2017 17:20:49

%S 2,29,59,227,251,269,293,419,443,677,683,773,821,827,1013,1187,1277,

%T 1301,1373,1451,1493,1523,1709,1733,1811,1901,1949,2027,2237,2243,

%U 2339,2357,2381,2477,2579,2693,2699,2909,3299,3371,3389,3413,3467

%N Primes of the form 2x^2 + 27y^2.

%C Discriminant = -216. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107161/b107161.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%t QuadPrimes2[2, 0, 27, 10000] (* see A106856 *)

%t With[{nn=50},Take[Union[Select[2#[[1]]+27#[[2]]&/@(Tuples[Range[ 0,nn],2]^2),PrimeQ]],nn]] (* _Harvey P. Dale_, Jun 15 2014 *)

%o (PARI) list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\2), w=2*x^2; for(y=0, sqrtint((lim-w)\27), if(isprime(t=w+27*y^2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 09 2017

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005

%E Terms, including b-file, checked by _Harvey P. Dale_, Jun 16 2014