login
Primes of the form 3x^2 + 55y^2.
1

%I #18 Sep 08 2022 08:45:34

%S 3,67,103,163,223,367,463,487,643,727,823,883,907,1087,1123,1303,1423,

%T 1483,1543,1567,1747,1783,2083,2143,2203,2347,2467,2707,2803,2887,

%U 3067,3463,3547,3727,3943,4027,4327,4423,4447,4603,4723,4783,4987

%N Primes of the form 3x^2 + 55y^2.

%C Discriminant = -660. See A139827 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A139868/b139868.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 The primes are congruent to {3, 67, 103, 163, 223, 247, 367, 427, 463, 487, 643} (mod 660).

%t QuadPrimes2[3, 0, 55, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(6000) | p mod 660 in {3, 67, 103, 163, 223, 247, 367, 427, 463, 487, 643}]; // _Vincenzo Librandi_, Jul 30 2012

%o (PARI) list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\3), w=3*x^2; for(y=0, sqrtint((lim-w)\55), if(isprime(t=w+55*y^2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Mar 07 2017

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008