cp's OEIS Frontend

A107003 Primes of the form 24n + 5.

%I A107003 #36 Aug 25 2025 19:11:06
%S A107003 5,29,53,101,149,173,197,269,293,317,389,461,509,557,653,677,701,773,
%T A107003 797,821,941,1013,1061,1109,1181,1229,1277,1301,1373,1493,1613,1637,
%U A107003 1709,1733,1877,1901,1949,1973,1997,2069,2141,2213,2237,2309,2333,2357,2381,2477
%N A107003 Primes of the form 24n + 5.
%C A107003 Primes of the form 5x^2+2xy+5y^2, with x and y any integer. Discriminant=-96. Also primes of the forms 5x^2+4xy+20y^2 and 5x^2+2xy+29y^2. See A140633. - _T. D. Noe_, May 19 2008
%C A107003 Also primes of the form -4*x^2+4*x*y+5*y^2, of discriminant -96 (as well as of the form 8*x^2+16*x*y+5*y^2). - Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (oscfalgan(AT)yahoo.es), Jun 28 2008
%D A107003 Z. I. Borevich and I. R. Shafarevich. Number Theory. Academic Press. 1966.
%H A107003 Vincenzo Librandi and Ray Chandler, <a href="/A107003/b107003.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi]
%H A107003 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 A107003 a(n) ~ 8n log n. - _Charles R Greathouse IV_, Dec 07 2014
%e A107003 29 is a member because we can write 29=-4*4^2+4*4*3+5*3^2 (or 29=8*1^2+16*1*1+5*1^2).
%t A107003 Union[QuadPrimes2[5, 2, 5, 10000], QuadPrimes2[5, -2, 5, 10000]] (* see A106856 *)
%t A107003 Select[24*Range[0,200]+5,PrimeQ] (* _Harvey P. Dale_, Aug 25 2025 *)
%o A107003 (PARI) select(n->n%24==5, primes(1000)) \\ _Charles R Greathouse IV_, Dec 07 2014
%Y A107003 Cf. A141373, A141375, A141376 (d = -96).
%K A107003 nonn,easy,changed
%O A107003 1,1
%A A107003 _T. D. Noe_, May 09 2005
%E A107003 Name and comment switched by _Charles R Greathouse IV_, Dec 07 2014
%E A107003 Edited by _N. J. A. Sloane_, Jul 14 2019