A107003 Primes of the form 24n + 5.

5, 29, 53, 101, 149, 173, 197, 269, 293, 317, 389, 461, 509, 557, 653, 677, 701, 773, 797, 821, 941, 1013, 1061, 1109, 1181, 1229, 1277, 1301, 1373, 1493, 1613, 1637, 1709, 1733, 1877, 1901, 1949, 1973, 1997, 2069, 2141, 2213, 2237, 2309, 2333, 2357, 2381, 2477

Offset: 1

Author

T. D. Noe, May 09 2005

Keywords

• nonn
• easy
• changed

Comments

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

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

Examples

			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).
		

References

• Z. I. Borevich and I. R. Shafarevich. Number Theory. Academic Press. 1966.

Links

• Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]
• N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

Crossrefs

Cf. A141373, A141375, A141376 (d = -96).

Programs

Mathematica

Union[QuadPrimes2[5, 2, 5, 10000], QuadPrimes2[5, -2, 5, 10000]] (* see A106856 *)
Select[24*Range[0,200]+5,PrimeQ] (* Harvey P. Dale, Aug 25 2025 *)

PARI

select(n->n%24==5, primes(1000)) \\ Charles R Greathouse IV, Dec 07 2014

Formula

a(n) ~ 8n log n. - Charles R Greathouse IV, Dec 07 2014

Extensions

Name and comment switched by Charles R Greathouse IV, Dec 07 2014

Edited by N. J. A. Sloane, Jul 14 2019