A139978 - OEIS

%I #16 Sep 08 2022 08:45:34

%S 5,157,197,277,397,557,613,653,733,757,853,997,1013,1213,1277,1373,

%T 1453,1493,1597,1613,1733,1973,2053,2213,2357,2437,2477,2557,2677,

%U 2797,2837,3037,3253,3557,3733,3797,3877,4013,4253,4357,4493,4637

%N Primes of the form 5x^2+152y^2.

%C Discriminant=-3040. See A139827 for more information.

%H Vincenzo Librandi and Ray Chandler, <a href="/A139978/b139978.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 {5, 77, 93, 157, 197, 213, 237, 253, 277, 397, 453, 517, 533, 557, 613, 653, 693, 733, 757, 837, 853, 917, 957, 973, 997, 1013, 1037, 1157, 1213, 1277, 1293, 1317, 1373, 1413, 1453, 1493, 1517, 1597, 1613, 1677, 1717, 1733, 1757, 1773, 1797, 1917, 1973, 2037, 2053, 2077, 2133, 2173, 2213, 2253, 2277, 2357, 2373, 2437, 2477, 2493, 2517, 2533, 2557, 2677, 2733, 2797, 2813, 2837, 2893, 2933, 2973, 3013, 3037} (mod 3040).

%t QuadPrimes2[5, 0, 152, 10000] (* see A106856 *)

%o (Magma) [p: p in PrimesUpTo(6000) | p mod 3040 in [5, 77, 93, 157, 197, 213, 237, 253, 277, 397, 453, 517, 533, 557, 613, 653, 693, 733, 757, 837, 853, 917, 957, 973, 997, 1013, 1037, 1157, 1213, 1277, 1293, 1317, 1373, 1413, 1453, 1493, 1517, 1597, 1613, 1677, 1717, 1733, 1757, 1773, 1797, 1917, 1973, 2037, 2053, 2077, 2133, 2173, 2213, 2253, 2277, 2357, 2373, 2437, 2477, 2493, 2517, 2533, 2557, 2677, 2733, 2797, 2813, 2837, 2893, 2933, 2973, 3013, 3037]]; // _Vincenzo Librandi_, Aug 03 2012

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 02 2008