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A107133 Primes of the form 4x^2 + 7y^2. 2


%S 7,11,23,43,67,71,79,107,127,151,163,179,191,211,239,263,331,347,359,

%T 379,431,443,463,487,491,499,547,571,599,631,659,683,739,743,751,823,

%U 827,863,883,907,911,919,947,967,991,1019,1031,1051,1087,1103,1163

%N Primes of the form 4x^2 + 7y^2.

%C Discriminant = -112. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107133/b107133.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)

%F Except for 7, the primes are congruent to {11, 15, 23} (mod 28). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[4, 0, 7, 10000] (* see A106856 *)

%o (PARI) list(lim)=my(v=List(),w,t); for(x=0, sqrtint(lim\4), w=4*x^2; for(y=1, sqrtint((lim-w)\7), if(isprime(t=w+7*y^2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 09 2017

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005

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Last modified January 22 07:39 EST 2020. Contains 331139 sequences. (Running on oeis4.)