A107178 - OEIS

%I #20 Sep 08 2022 08:45:18

%S 7,17,47,73,97,103,167,223,257,313,353,367,383,433,503,577,593,607,

%T 647,727,857,887,937,983,1063,1097,1153,1193,1217,1223,1433,1447,1487,

%U 1543,1553,1567,1657,1697,1753,1777,1783,1823,1847,1993,2063,2113

%N Primes of the form 7x^2 + 10y^2.

%C Discriminant=-280. See A107132 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A107178/b107178.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 {7, 17, 33, 47, 73, 87, 97, 103, 143, 153, 167, 223, 257} (mod 280). - _T. D. Noe_, May 02 2008

%t QuadPrimes2[7, 0, 10, 10000] (* see A106856 *)

%o (Magma) [ p: p in PrimesUpTo(3000) | p mod 280 in {7, 17, 33, 47, 73, 87, 97, 103, 143, 153, 167, 223, 257} ]; // _Vincenzo Librandi_, Jul 26 2012

%o (PARI) list(lim)=my(v=List(),w,t); for(x=1, sqrtint(lim\7), w=7*x^2; for(y=0, sqrtint((lim-w)\10), if(isprime(t=w+10*y^2), listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Feb 10 2017

%Y Cf. A139827.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 13 2005